L'obiettivo di questo progetto è quello di trovare le similarità tra le pathway biologiche utilizzando l'algoritmo SimRank.
I dati che si hanno a disposizioni sono presenti all'interno dei seguenti file:
SimRank è una misura di similarità generale, basata su un modello di teoria dei grafi semplice e intuitivo. SimRank è applicabile in qualsiasi dominio con relazioni oggetto-oggetto, che misura la somiglianza del contesto strutturale in cui si verificano gli oggetti, in base alle loro relazioni con altri oggetti. In effetti, SimRank è una misura che dice "due oggetti sono considerati simili se sono referenziati da oggetti simili". Sebbene SimRank sia ampiamente adottato, può produrre punteggi di somiglianza irragionevoli che sono influenzati da diversi fattori.
La proposta originale di SimRank suggeriva di scegliere il fattore di decadimento $C = 0,8$ e un numero fisso $K = 5$ di iterazioni da eseguire. Tuttavia, la recente ricerca di D. Lizorkin, P. Velikhov, M. Grinev e D. Turdako http://modis.ispras.ru/Lizorkin/Publications/simrank_accuracy.pdf ha mostrato che i valori dati per $C$ e $K$ generalmente implicano punteggi relativamente bassi dei SimRank calcolati in modo iterativo. Per garantire risultati di calcolo più accurati, quest'ultimo documento suggerisce di utilizzare un fattore di decadimento più piccolo (in particolare, $C = 0,6$) o di eseguire più iterazioni.
Per un nodo $v$ in un grafo orientato, indichiamo con $I(v)$ e $O(v)$ l'insieme dei vicini in e out di $v$, rispettivamente. I singoli in-neighbors sono indicati come $I_i(v)$, per $1 \le i \le \left|I(v)\right|$, e i singoli out-neighbors sono indicati come $O_i(v)$, per $1 \le i \le \left|O(v)\right|$.
Indichiamo la somiglianza tra gli oggetti $a$ e $b$ con $s(a, b) \in [0, 1]$. Seguendo la motivazione precedente, viene scritta un'equazione ricorsiva per $s(a, b)$.
Se $a = b$ allora $s(a, b)$ è definito come $1$.
Altrimenti:
$s(a, b) = \frac{C}{\left|I(a)\right| \left|I(b)\right|} \sum_{i=1}^{\left|I(a)\right|}\sum_{j=1}^{\left|I(b)\right|} s(I_i(a), I_j(b))$
dove $C$ è una costante tra $0$ e $1$.
Un problema qui è che $a$ o $b$ potrebbero non avere alcun in-vicino.
Poiché non c'è modo di dedurre alcuna somiglianza tra $a$ e $b$ in questo caso, la somiglianza è impostata su $s(a, b) = 0$ , quindi la somma nell'equazione precedente è definita come $0$ quando $I(a) = \emptyset$ o $I(b) = \emptyset$ .
È stato realizzato un programma in Scala che utilizza Spark, per il calcolo distribuito, che calcola il SimRank utilizzando la definizione sopra, di seguito è riportato un esempio.
Esempio
Prima di tutto bisogna compilare utilizzando maven.
$ mvn package install
A questo punto è possibile eseguire l'esempio utilizzando l'istruzione successiva.
!spark-submit --class it.unict.gigig.SimRankClassic target/simrank-1.0-SNAPSHOT.jar prova.txt 0.6 5
2021-07-02 12:51:41 WARN Utils:66 - Your hostname, gigi-g-ThinkPad-T410 resolves to a loopback address: 127.0.1.1; using 192.168.1.21 instead (on interface wlp3s0)
2021-07-02 12:51:41 WARN Utils:66 - Set SPARK_LOCAL_IP if you need to bind to another address
2021-07-02 12:51:42 INFO SparkContext:54 - Running Spark version 2.3.0
2021-07-02 12:51:42 INFO SparkContext:54 - Submitted application: learn
2021-07-02 12:51:42 INFO SecurityManager:54 - Changing view acls to: gigi-g
2021-07-02 12:51:42 INFO SecurityManager:54 - Changing modify acls to: gigi-g
2021-07-02 12:51:42 INFO SecurityManager:54 - Changing view acls groups to:
2021-07-02 12:51:42 INFO SecurityManager:54 - Changing modify acls groups to:
2021-07-02 12:51:42 INFO SecurityManager:54 - SecurityManager: authentication disabled; ui acls disabled; users with view permissions: Set(gigi-g); groups with view permissions: Set(); users with modify permissions: Set(gigi-g); groups with modify permissions: Set()
2021-07-02 12:51:43 INFO Utils:54 - Successfully started service 'sparkDriver' on port 40453.
2021-07-02 12:51:43 INFO SparkEnv:54 - Registering MapOutputTracker
2021-07-02 12:51:43 INFO SparkEnv:54 - Registering BlockManagerMaster
2021-07-02 12:51:43 INFO BlockManagerMasterEndpoint:54 - Using org.apache.spark.storage.DefaultTopologyMapper for getting topology information
2021-07-02 12:51:43 INFO BlockManagerMasterEndpoint:54 - BlockManagerMasterEndpoint up
2021-07-02 12:51:43 INFO DiskBlockManager:54 - Created local directory at /tmp/blockmgr-2f9a83b9-1363-412d-b6f1-aace7b0cec33
2021-07-02 12:51:43 INFO MemoryStore:54 - MemoryStore started with capacity 366.3 MB
2021-07-02 12:51:43 INFO SparkEnv:54 - Registering OutputCommitCoordinator
2021-07-02 12:51:43 INFO log:192 - Logging initialized @2721ms
2021-07-02 12:51:43 INFO Server:346 - jetty-9.3.z-SNAPSHOT
2021-07-02 12:51:43 INFO Server:414 - Started @2879ms
2021-07-02 12:51:43 INFO AbstractConnector:278 - Started ServerConnector@25dd8365{HTTP/1.1,[http/1.1]}{0.0.0.0:4040}
2021-07-02 12:51:43 INFO Utils:54 - Successfully started service 'SparkUI' on port 4040.
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@750fe12e{/jobs,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@402f80f5{/jobs/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@5bbc9f97{/jobs/job,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@41382722{/jobs/job/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@7dac3fd8{/stages,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@425357dd{/stages/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@2102a4d5{/stages/stage,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@65f87a2c{/stages/stage/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@51684e4a{/stages/pool,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@6ce1f601{/stages/pool/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@38875e7d{/storage,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@1e886a5b{/storage/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@d816dde{/storage/rdd,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@6e33c391{/storage/rdd/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@6c451c9c{/environment,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@31c269fd{/environment/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@372b0d86{/executors,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@47747fb9{/executors/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@3113a37{/executors/threadDump,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@213e3629{/executors/threadDump/json,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@4e9658b5{/static,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@5305c37d{/,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@51a06cbe{/api,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@66d23e4a{/jobs/job/kill,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@36ac8a63{/stages/stage/kill,null,AVAILABLE,@Spark}
2021-07-02 12:51:43 INFO SparkUI:54 - Bound SparkUI to 0.0.0.0, and started at http://Host-004.home:4040
2021-07-02 12:51:44 INFO SparkContext:54 - Added JAR file:/home/gigi-g/BigData/simrank/target/simrank-1.0-SNAPSHOT.jar at spark://Host-004.home:40453/jars/simrank-1.0-SNAPSHOT.jar with timestamp 1625223104159
2021-07-02 12:51:44 INFO Executor:54 - Starting executor ID driver on host localhost
2021-07-02 12:51:44 INFO Utils:54 - Successfully started service 'org.apache.spark.network.netty.NettyBlockTransferService' on port 44421.
2021-07-02 12:51:44 INFO NettyBlockTransferService:54 - Server created on Host-004.home:44421
2021-07-02 12:51:44 INFO BlockManager:54 - Using org.apache.spark.storage.RandomBlockReplicationPolicy for block replication policy
2021-07-02 12:51:44 INFO BlockManagerMaster:54 - Registering BlockManager BlockManagerId(driver, Host-004.home, 44421, None)
2021-07-02 12:51:44 INFO BlockManagerMasterEndpoint:54 - Registering block manager Host-004.home:44421 with 366.3 MB RAM, BlockManagerId(driver, Host-004.home, 44421, None)
2021-07-02 12:51:44 INFO BlockManagerMaster:54 - Registered BlockManager BlockManagerId(driver, Host-004.home, 44421, None)
2021-07-02 12:51:44 INFO BlockManager:54 - Initialized BlockManager: BlockManagerId(driver, Host-004.home, 44421, None)
2021-07-02 12:51:44 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@d02f8d{/metrics/json,null,AVAILABLE,@Spark}
(0,0)=1.0
(0,1)=0.0
(0,2)=0.0
(0,3)=0.0
(1,0)=0.0
(1,1)=1.0
(1,2)=0.04030223
(1,3)=0.16120906
(2,0)=0.0
(2,1)=0.04030223
(2,2)=1.0
(2,3)=0.012090621
(3,0)=0.0
(3,1)=0.16120906
(3,2)=0.012090621
(3,3)=1.0
Il risultato ottenuto differisce da quello reale per il problema mostrato nella premessa, la soluzione iterativa restituisce un valore più basso di quello originale.
Sia $\mathbf{S}$ la matrice di somiglianza la cui voce $[\mathbf{S}]_{a,b}$ denota il punteggio di somiglianza $s(a, b)$, e $\mathbf{A}$ sia la colonna normalizzata [[matrice di adiacenza]] la cui voce $[\mathbf{A}]_{a,b}=\frac{1}{|\mathcal{I}(b)|}$ se c'è un arco da $a$ a $b$ e 0 altrimenti. Quindi, nelle notazioni matriciali, SimRank può essere formulato come:
${{\mathbf{S}}}= \max\{C\cdot (\mathbf{A}^{T} \cdot {{\mathbf{S}}}\cdot {{\mathbf{A}}} ) , {{\mathbf{I}}}\},$
dove $\mathbf{I}$ è una matrice identità.
Esempio
Seguendo la definizione riportata sopra effettuiamo il calcolo utilizzando la notazione matriciale con Scala, Spark e Hadoop.
!hdfs dfs -rm -R /simrank
!hdfs dfs -mkdir /simrank
!hdfs dfs -mkdir /simrank/input
!hdfs dfs -copyFromLocal prova.txt /simrank/input/prova.txt
21/07/02 13:05:04 INFO fs.TrashPolicyDefault: Namenode trash configuration: Deletion interval = 0 minutes, Emptier interval = 0 minutes. Deleted /simrank
!hdfs dfs -ls /simrank/input/
Found 1 items -rw-r--r-- 1 gigi-g supergroup 36 2021-07-02 13:05 /simrank/input/prova.txt
!spark-submit --class it.unict.gigig.SimRankMatrix target/simrank-1.0-SNAPSHOT.jar prova.txt 0.6 5
2021-07-02 13:06:14 WARN Utils:66 - Your hostname, gigi-g-ThinkPad-T410 resolves to a loopback address: 127.0.1.1; using 192.168.1.21 instead (on interface wlp3s0)
2021-07-02 13:06:14 WARN Utils:66 - Set SPARK_LOCAL_IP if you need to bind to another address
2021-07-02 13:06:14 INFO SparkContext:54 - Running Spark version 2.3.0
2021-07-02 13:06:14 INFO SparkContext:54 - Submitted application: learn
2021-07-02 13:06:14 INFO SecurityManager:54 - Changing view acls to: gigi-g
2021-07-02 13:06:14 INFO SecurityManager:54 - Changing modify acls to: gigi-g
2021-07-02 13:06:14 INFO SecurityManager:54 - Changing view acls groups to:
2021-07-02 13:06:14 INFO SecurityManager:54 - Changing modify acls groups to:
2021-07-02 13:06:14 INFO SecurityManager:54 - SecurityManager: authentication disabled; ui acls disabled; users with view permissions: Set(gigi-g); groups with view permissions: Set(); users with modify permissions: Set(gigi-g); groups with modify permissions: Set()
2021-07-02 13:06:15 INFO Utils:54 - Successfully started service 'sparkDriver' on port 40903.
2021-07-02 13:06:15 INFO SparkEnv:54 - Registering MapOutputTracker
2021-07-02 13:06:15 INFO SparkEnv:54 - Registering BlockManagerMaster
2021-07-02 13:06:15 INFO BlockManagerMasterEndpoint:54 - Using org.apache.spark.storage.DefaultTopologyMapper for getting topology information
2021-07-02 13:06:15 INFO BlockManagerMasterEndpoint:54 - BlockManagerMasterEndpoint up
2021-07-02 13:06:15 INFO DiskBlockManager:54 - Created local directory at /tmp/blockmgr-2bf682eb-d43f-43b0-bfbf-10429e6e95ec
2021-07-02 13:06:15 INFO MemoryStore:54 - MemoryStore started with capacity 366.3 MB
2021-07-02 13:06:15 INFO SparkEnv:54 - Registering OutputCommitCoordinator
2021-07-02 13:06:15 INFO log:192 - Logging initialized @2664ms
2021-07-02 13:06:15 INFO Server:346 - jetty-9.3.z-SNAPSHOT
2021-07-02 13:06:15 INFO Server:414 - Started @2819ms
2021-07-02 13:06:15 INFO AbstractConnector:278 - Started ServerConnector@41a0497d{HTTP/1.1,[http/1.1]}{0.0.0.0:4040}
2021-07-02 13:06:15 INFO Utils:54 - Successfully started service 'SparkUI' on port 4040.
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@1c25b8a7{/jobs,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@77b7ffa4{/jobs/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@5ed190be{/jobs/job,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@5bbc9f97{/jobs/job/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@133e019b{/stages,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@41382722{/stages/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@7dac3fd8{/stages/stage,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@210386e0{/stages/stage/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@3d4d3fe7{/stages/pool,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@65f87a2c{/stages/pool/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@51684e4a{/storage,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@6ce1f601{/storage/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@38875e7d{/storage/rdd,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@1e886a5b{/storage/rdd/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@d816dde{/environment,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@6e33c391{/environment/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@6c451c9c{/executors,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@31c269fd{/executors/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@372b0d86{/executors/threadDump,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@47747fb9{/executors/threadDump/json,null,AVAILABLE,@Spark}
2021-07-02 13:06:15 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@3113a37{/static,null,AVAILABLE,@Spark}
2021-07-02 13:06:16 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@f5c79a6{/,null,AVAILABLE,@Spark}
2021-07-02 13:06:16 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@669253b7{/api,null,AVAILABLE,@Spark}
2021-07-02 13:06:16 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@49a64d82{/jobs/job/kill,null,AVAILABLE,@Spark}
2021-07-02 13:06:16 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@344561e0{/stages/stage/kill,null,AVAILABLE,@Spark}
2021-07-02 13:06:16 INFO SparkUI:54 - Bound SparkUI to 0.0.0.0, and started at http://Host-004.home:4040
2021-07-02 13:06:16 INFO SparkContext:54 - Added JAR file:/home/gigi-g/BigData/simrank/target/simrank-1.0-SNAPSHOT.jar at spark://Host-004.home:40903/jars/simrank-1.0-SNAPSHOT.jar with timestamp 1625223976238
2021-07-02 13:06:16 INFO Executor:54 - Starting executor ID driver on host localhost
2021-07-02 13:06:16 INFO Utils:54 - Successfully started service 'org.apache.spark.network.netty.NettyBlockTransferService' on port 43829.
2021-07-02 13:06:16 INFO NettyBlockTransferService:54 - Server created on Host-004.home:43829
2021-07-02 13:06:16 INFO BlockManager:54 - Using org.apache.spark.storage.RandomBlockReplicationPolicy for block replication policy
2021-07-02 13:06:16 INFO BlockManagerMaster:54 - Registering BlockManager BlockManagerId(driver, Host-004.home, 43829, None)
2021-07-02 13:06:16 INFO BlockManagerMasterEndpoint:54 - Registering block manager Host-004.home:43829 with 366.3 MB RAM, BlockManagerId(driver, Host-004.home, 43829, None)
2021-07-02 13:06:16 INFO BlockManagerMaster:54 - Registered BlockManager BlockManagerId(driver, Host-004.home, 43829, None)
2021-07-02 13:06:16 INFO BlockManager:54 - Initialized BlockManager: BlockManagerId(driver, Host-004.home, 43829, None)
2021-07-02 13:06:16 INFO ContextHandler:781 - Started o.s.j.s.ServletContextHandler@6f012914{/metrics/json,null,AVAILABLE,@Spark}
!hdfs dfs -cat /simrank/output/part-00000
(0,0,1.0) (0,1,0.0) (0,1,0.0) (0,1,0.0) (1,0,0.0) (1,1,1.0) (1,2,0.05016002) (1,3,0.20144004) (2,0,0.0) (2,1,0.05016002) (2,2,1.0) (2,3,0.014880006) (3,0,0.0) (3,1,0.20144004) (3,2,0.014880006) (3,3,1.0)
Dopo aver introdotto il SimRank e alcune delle sue implementazioni, di seguito sono importate le librerie e le funzioni necessarie per ogni cella.
Nella risoluzione del problema per il calcolo del SimRank non verranno utilizzate le implementazioni in Scala, questo perché sono più efficienti se utilizzate in un cluster dato che si è utilizzato Spark e Hadoop. Per semplicità verrà utilizzata la libreria networkx di Python, che ha al proprio interno una funzione che permette di calcolare il SimRank.
%matplotlib inline
import numpy as np
import scipy.io as sio
import scipy.sparse as spsp
import matplotlib.pyplot as plt
from sklearn.preprocessing import normalize
from pandas import read_csv
import pandas as pd
import networkx as nx
from scipy.io import mmwrite
from scipy.io import mmwrite
from numpy import array
Questa è un'altra implementazione che riesce a stimare il valore reale del SimRank in grafi molto grandi.
L'implementazione non è stata fatta da me, per questo non è riportato il codice sorgente all'interno della repository di GitHub, ma può essere consultato al seguente link.
Di seguito è riportato un esempio, successivamente verrà utilizzato anche per verificare se è possibile utilizzare questa implementazione veloce per risolvere il problema delle similarità tra le pathway biologiche.
graph_filename_mat = "./data/delaunay_n12.mat"
c = 0.6
num_iter = 5
W = sio.loadmat(graph_filename_mat)['Problem'][0][0][2]
C = normalize(W, norm='l1', axis=0)
C = np.sqrt(c) * C
print("Number of vertices =", C.shape[0])
print("Number of edges =", C.nnz / 2)
Number of vertices = 4096 Number of edges = 12264.0
def simrank_naive(W, k):
S = np.eye(max(W.shape))
for i in range(int(k)):
S = W.T.dot(S)
S = W.T.dot(S.T)
for j in range(max(W.shape)):
S[j,j] = 1
return S
S_true = simrank_naive(C, num_iter)
S_true
array([[1.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,
1.86806916e-05, 2.49471844e-05, 6.05660981e-05],
[0.00000000e+00, 1.00000000e+00, 0.00000000e+00, ...,
2.60915485e-05, 1.16690326e-05, 6.32475181e-06],
[0.00000000e+00, 0.00000000e+00, 1.00000000e+00, ...,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
...,
[1.86806916e-05, 2.60915485e-05, 0.00000000e+00, ...,
1.00000000e+00, 9.48666394e-02, 7.22038713e-02],
[2.49471844e-05, 1.16690326e-05, 0.00000000e+00, ...,
9.48666394e-02, 1.00000000e+00, 9.22689284e-02],
[6.05660981e-05, 6.32475181e-06, 0.00000000e+00, ...,
7.22038713e-02, 9.22689284e-02, 1.00000000e+00]])
L'approssimazione segue la seguente equazione:
$$ \tilde{S} = I + C^{\top}C - \text{diag}(C^{\top}C) + UDU^{\top}. $$La matrice $C$ è la matrice di adiacenza normalizzata per colonne e scalata per $\sqrt{c}$ del grafo. La matrice $U$ è di basso rango e la matrice $D$ è diagonale.
num_iter = 50
rank = 100
oversampl = 0
U_file = "./data/U_del12.csv"
d_file = "./data/d_del12.csv"
graph_filename_mtx = graph_filename_mat.split("/")[2].split(".")[0] + ".mtx"
graph_filename_mtx = "/".join(graph_filename_mat.split("/")[0:2]) + "/" + graph_filename_mtx
!./simrank_lowrank/build/simrank_lowrank -g $graph_filename_mtx -i $num_iter -c $c -r $rank -s $oversampl -u $U_file -d $d_file
Reading graph from ./data/delaunay_n12.mtx... Number of vertices = 4096 Number of edges = 12264 Reading graph from ./data/delaunay_n12.mtx...Done Compute low rank approximation of SimRank... Iteration 1 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 2 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 3 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 4 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 5 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 6 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 7 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 8 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 9 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 10 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 11 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 12 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 13 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 14 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 15 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 16 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 17 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 18 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 19 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 20 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 21 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 22 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 23 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 24 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 25 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 26 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 27 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 28 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 29 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 30 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 31 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 32 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 33 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 34 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 35 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 36 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 37 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 38 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 39 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 40 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 41 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 42 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 43 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 44 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 45 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 46 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 47 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 48 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 49 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 50 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Compute low rank approximation of SimRank... Done Saving lowrank matrices... Saving lowrank matrices...Done Elapsed time = 86.428369
U = read_csv("./data/U_del12.csv", header=None)
d = np.array(read_csv("./data/d_del12.csv", header=None))
D = np.diag(d[:, 0])
CTC = C.T.dot(C)
S_appr = np.eye(C.shape[0]) + CTC - np.diag(CTC.diagonal()) + U.dot(D).dot(U.T)
S_appr
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... | 4086 | 4087 | 4088 | 4089 | 4090 | 4091 | 4092 | 4093 | 4094 | 4095 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.003560 | -0.000390 | -0.000266 | 0.000720 | 0.000338 | -0.000476 | 0.001024 | 0.000419 | -0.000203 | 0.000321 | ... | 0.000291 | 0.000336 | -0.000090 | 0.000137 | 0.000221 | -0.000014 | 0.000014 | 0.000277 | -0.000020 | 0.000202 |
| 1 | -0.000390 | 1.004995 | 0.000803 | 0.000913 | 0.000112 | -0.000151 | -0.000549 | -0.000155 | -0.000104 | 0.000104 | ... | 0.000834 | 0.000773 | 0.000506 | 0.000363 | 0.000698 | 0.000515 | 0.000671 | 0.000156 | 0.000160 | 0.000547 |
| 2 | -0.000266 | 0.000803 | 1.005271 | -0.000181 | 0.000500 | -0.000353 | -0.000120 | -0.000264 | -0.000468 | -0.000076 | ... | 0.000721 | 0.000587 | -0.000130 | -0.000366 | -0.000187 | -0.000190 | -0.000345 | 0.000449 | 0.000353 | 0.000261 |
| 3 | 0.000720 | 0.000913 | -0.000181 | 1.007045 | 0.000371 | 0.000621 | 0.000227 | 0.000464 | -0.000481 | 0.000547 | ... | -0.002072 | -0.001333 | -0.000953 | -0.000685 | -0.001118 | -0.000342 | -0.000593 | -0.001342 | -0.001337 | -0.001111 |
| 4 | 0.000338 | 0.000112 | 0.000500 | 0.000371 | 1.006790 | -0.000213 | -0.000292 | -0.000564 | 0.000414 | 0.000354 | ... | 0.000763 | 0.000628 | 0.000356 | 0.000389 | 0.000532 | 0.000304 | -0.000238 | 0.000896 | 0.000805 | 0.000422 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 4091 | -0.000014 | 0.000515 | -0.000190 | -0.000342 | 0.000304 | 0.000402 | -0.000247 | 0.000274 | 0.000311 | 0.000434 | ... | 0.002776 | 0.001707 | 0.001381 | 0.002505 | 0.014933 | 1.004900 | 0.033599 | 0.054613 | 0.023609 | 0.003854 |
| 4092 | 0.000014 | 0.000671 | -0.000345 | -0.000593 | -0.000238 | 0.000077 | -0.000631 | 0.000095 | 0.000177 | 0.000272 | ... | 0.003391 | 0.002262 | 0.002353 | 0.003843 | 0.024024 | 0.033599 | 1.006916 | 0.026926 | 0.021583 | 0.004871 |
| 4093 | 0.000277 | 0.000156 | 0.000449 | -0.001342 | 0.000896 | 0.000667 | 0.000537 | -0.000228 | 0.000344 | 0.000420 | ... | 0.006493 | 0.005009 | 0.003496 | 0.003961 | 0.039817 | 0.054613 | 0.026926 | 1.009330 | 0.067039 | 0.044703 |
| 4094 | -0.000020 | 0.000160 | 0.000353 | -0.001337 | 0.000805 | 0.000343 | 0.000155 | -0.000662 | 0.000083 | 0.000271 | ... | 0.036601 | 0.039434 | 0.020989 | 0.027765 | 0.032640 | 0.023609 | 0.021583 | 0.067039 | 1.007440 | 0.066892 |
| 4095 | 0.000202 | 0.000547 | 0.000261 | -0.001111 | 0.000422 | 0.000035 | 0.000514 | -0.000130 | 0.000313 | 0.000838 | ... | 0.081858 | 0.027350 | 0.004203 | 0.004054 | 0.039749 | 0.003854 | 0.004871 | 0.044703 | 0.066892 | 1.008350 |
4096 rows × 4096 columns
print("Difference in Frobenius norm =", np.linalg.norm(S_appr - S_true) / np.linalg.norm(S_true))
print("Difference in l2 norm =", np.linalg.norm(S_appr - S_true, 2) / np.linalg.norm(S_true, 2))
Difference in Frobenius norm = 0.07517952206285075 Difference in l2 norm = 0.26023382348950824
Di seguito è riportato un esempio del calcolo del SimRank utilizzando networkx.
g = nx.read_edgelist('./data/prova.txt', nodetype=int,
data=(('weight',float),), create_using=nx.DiGraph())
print(g.edges(data=True))
[(0, 1, {'weight': 1.0}), (0, 3, {'weight': 1.0}), (1, 2, {'weight': 1.0}), (3, 1, {'weight': 1.0}), (2, 1, {'weight': 1.0}), (2, 3, {'weight': 1.0})]
pos = nx.spiral_layout(g)
nx.draw(g, pos)
plt.show()
nx.adjacency_matrix(g, nodelist=[0, 1, 2, 3]).todense()
matrix([[0., 1., 0., 1.],
[0., 0., 1., 0.],
[0., 1., 0., 1.],
[0., 1., 0., 0.]])
W = nx.adjacency_matrix(g, nodelist=[0, 1, 2, 3])
C = normalize(W, norm='l1', axis=0)
C = np.sqrt(c) * C
mmwrite("./data/prova.mtx", nx.adjacency_matrix(g, nodelist=[0, 1, 2, 3]))
c = 0.6
num_iter = 12
rank = 1
oversampl = 0.0001
U_file = "./data/U_prova.csv"
d_file = "./data/d_prova.csv"
graph_filename_mtx = "./data/prova.mtx"
!./simrank_lowrank/build/simrank_lowrank -g $graph_filename_mtx -i $num_iter -c $c -r $rank -s $oversampl -u $U_file -d $d_file
Reading graph from ./data/prova.mtx... Number of vertices = 4 Number of edges = 6 Reading graph from ./data/prova.mtx...Done Compute low rank approximation of SimRank... Iteration 1 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 2 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 3 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 4 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 5 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 6 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 7 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 8 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 9 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 10 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 11 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 12 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Compute low rank approximation of SimRank... Done Saving lowrank matrices... Saving lowrank matrices...Done Elapsed time = 0.001763
U = read_csv("./data/U_prova.csv", header=None)
d = np.array(read_csv("./data/d_prova.csv", header=None))
D = np.diag(d[:, 0])
CTC = C.T.dot(C)
S_appr = np.eye(C.shape[0]) + CTC - np.diag(CTC.diagonal()) + U.dot(D).dot(U.T)
S_appr
| 0 | 1 | 2 | 3 | |
|---|---|---|---|---|
| 0 | 0.999980 | 0.000046 | -0.000665 | 0.000654 |
| 1 | 0.000046 | 0.999893 | 0.001534 | 0.198492 |
| 2 | -0.000665 | 0.001534 | 0.978024 | 0.021594 |
| 3 | 0.000654 | 0.198492 | 0.021594 | 0.978781 |
sim = nx.simrank_similarity(g, importance_factor=0.6, max_iterations=5, tolerance=0.0001)
simr = [[sim[u][v] for v in sorted(sim[u])] for u in sorted(sim)]
S_true = pd.DataFrame(simr, columns = [0,1,2,3])
S_true
| 0 | 1 | 2 | 3 | |
|---|---|---|---|---|
| 0 | 1.0 | 0.00000 | 0.00000 | 0.00000 |
| 1 | 0.0 | 1.00000 | 0.05016 | 0.20144 |
| 2 | 0.0 | 0.05016 | 1.00000 | 0.01488 |
| 3 | 0.0 | 0.20144 | 0.01488 | 1.00000 |
simrank_naive(C, 5)
array([[1. , 0. , 0. , 0. ],
[0. , 1. , 0.05016, 0.20144],
[0. , 0.05016, 1. , 0.01488],
[0. , 0.20144, 0.01488, 1. ]])
print("Difference in Frobenius norm =", np.linalg.norm(S_appr - S_true) / np.linalg.norm(S_true))
print("Difference in l2 norm =", np.linalg.norm(S_appr - S_true, 2) / np.linalg.norm(S_true, 2))
Difference in Frobenius norm = 0.03758011486837641 Difference in l2 norm = 0.0504982243226882
Prima di tutto creaiamo il grafo utilizzando tutti gli edges che sono presenti all'interno del file ./data/gene_edges.tsv.
g = nx.read_edgelist('./data/gene_edges.tsv', nodetype=int,
data = (('weight',float),), create_using=nx.DiGraph())
print(g.edges(data=True))
[(3640, 51289, {'weight': 1.0}), (3640, 122042, {'weight': 1.0}), (3640, 339403, {'weight': 1.0}), (3640, 59350, {'weight': 1.0}), (51289, 1956, {'weight': 1.0}), (284217, 3680, {'weight': 1.0}), (284217, 3696, {'weight': 1.0}), (284217, 3674, {'weight': 1.0}), (284217, 3675, {'weight': 1.0}), (284217, 3676, {'weight': 1.0}), (284217, 3655, {'weight': 1.0}), (284217, 3678, {'weight': 1.0}), (284217, 3679, {'weight': 1.0}), (284217, 22987, {'weight': 1.0}), (284217, 22801, {'weight': 1.0}), (284217, 3690, {'weight': 1.0}), (284217, 3691, {'weight': 1.0}), (284217, 3693, {'weight': 1.0}), (284217, 9899, {'weight': 1.0}), (284217, 3694, {'weight': 1.0}), (284217, 3672, {'weight': 1.0}), (284217, 3695, {'weight': 1.0}), (284217, 3673, {'weight': 1.0}), (284217, 960, {'weight': 1.0}), (284217, 3685, {'weight': 1.0}), (284217, 8516, {'weight': 1.0}), (284217, 9900, {'weight': 1.0}), (284217, 3688, {'weight': 1.0}), (284217, 8515, {'weight': 1.0}), (284217, 1605, {'weight': 1.0}), (284217, 5747, {'weight': 1.0}), (3680, 9564, {'weight': 1.0}), (3680, 1399, {'weight': 1.0}), (3680, 1398, {'weight': 1.0}), (3680, 7412, {'weight': 1.0}), (3680, 6714, {'weight': 1.0}), (3680, 5747, {'weight': 1.0}), (3696, 9564, {'weight': 1.0}), (3696, 1399, {'weight': 1.0}), (3696, 1398, {'weight': 1.0}), (3696, 6714, {'weight': 1.0}), (3696, 5747, {'weight': 1.0}), (3674, 9564, {'weight': 1.0}), (3674, 1399, {'weight': 1.0}), (3674, 1398, {'weight': 1.0}), (3674, 10672, {'weight': 1.0}), (3674, 6714, {'weight': 1.0}), (3674, 5747, {'weight': 1.0}), (3675, 9564, {'weight': 1.0}), (3675, 1399, {'weight': 1.0}), (3675, 1398, {'weight': 1.0}), (3675, 6714, {'weight': 1.0}), (3675, 5747, {'weight': 1.0}), (3676, 9564, {'weight': 1.0}), (3676, 1399, {'weight': 1.0}), (3676, 1398, {'weight': 1.0}), (3676, 7412, {'weight': 1.0}), (3676, 6714, {'weight': 1.0}), (3676, 5747, {'weight': 1.0}), (3655, 9564, {'weight': 1.0}), (3655, 1399, {'weight': 1.0}), (3655, 1398, {'weight': 1.0}), (3655, 6714, {'weight': 1.0}), (3655, 5747, {'weight': 1.0}), (3678, 9564, {'weight': 1.0}), (3678, 1399, {'weight': 1.0}), (3678, 1398, {'weight': 1.0}), (3678, 6714, {'weight': 1.0}), (3678, 5747, {'weight': 1.0}), (3679, 9564, {'weight': 1.0}), (3679, 1399, {'weight': 1.0}), (3679, 1398, {'weight': 1.0}), (3679, 6714, {'weight': 1.0}), (3679, 5747, {'weight': 1.0}), (22801, 9564, {'weight': 1.0}), (22801, 1399, {'weight': 1.0}), (22801, 1398, {'weight': 1.0}), (22801, 6714, {'weight': 1.0}), (22801, 5747, {'weight': 1.0}), (3690, 9564, {'weight': 1.0}), (3690, 4893, {'weight': 1.0}), (3690, 3265, {'weight': 1.0}), (3690, 1399, {'weight': 1.0}), (3690, 1398, {'weight': 1.0}), (3690, 5335, {'weight': 1.0}), (3690, 5336, {'weight': 1.0}), (3690, 10672, {'weight': 1.0}), (3690, 5330, {'weight': 1.0}), (3690, 5331, {'weight': 1.0}), (3690, 5332, {'weight': 1.0}), (3690, 113026, {'weight': 1.0}), (3690, 5333, {'weight': 1.0}), (3690, 23236, {'weight': 1.0}), (3690, 84812, {'weight': 1.0}), (3690, 51196, {'weight': 1.0}), (3690, 89869, {'weight': 1.0}), (3690, 6714, {'weight': 1.0}), (3690, 5747, {'weight': 1.0}), (3690, 3845, {'weight': 1.0}), (3691, 9564, {'weight': 1.0}), (3691, 1399, {'weight': 1.0}), (3691, 1398, {'weight': 1.0}), (3691, 6714, {'weight': 1.0}), (3691, 5747, {'weight': 1.0}), (3693, 9564, {'weight': 1.0}), (3693, 1399, {'weight': 1.0}), (3693, 1398, {'weight': 1.0}), (3693, 6714, {'weight': 1.0}), (3693, 5747, {'weight': 1.0}), (3694, 9564, {'weight': 1.0}), (3694, 1399, {'weight': 1.0}), (3694, 1398, {'weight': 1.0}), (3694, 6714, {'weight': 1.0}), (3694, 5747, {'weight': 1.0}), (3672, 9564, {'weight': 1.0}), (3672, 1399, {'weight': 1.0}), (3672, 1398, {'weight': 1.0}), (3672, 6714, {'weight': 1.0}), (3672, 5747, {'weight': 1.0}), (3695, 9564, {'weight': 1.0}), (3695, 1399, {'weight': 1.0}), (3695, 1398, {'weight': 1.0}), (3695, 6714, {'weight': 1.0}), (3695, 5747, {'weight': 1.0}), (3673, 9564, {'weight': 1.0}), (3673, 5295, {'weight': 1.0}), (3673, 5296, {'weight': 1.0}), (3673, 1399, {'weight': 1.0}), (3673, 1398, {'weight': 1.0}), (3673, 8503, {'weight': 1.0}), (3673, 5290, {'weight': 1.0}), (3673, 5291, {'weight': 1.0}), (3673, 6714, {'weight': 1.0}), (3673, 5747, {'weight': 1.0}), (3673, 5293, {'weight': 1.0}), (3685, 9564, {'weight': 1.0}), (3685, 5330, {'weight': 1.0}), (3685, 5331, {'weight': 1.0}), (3685, 5332, {'weight': 1.0}), (3685, 113026, {'weight': 1.0}), (3685, 5333, {'weight': 1.0}), (3685, 4893, {'weight': 1.0}), (3685, 3265, {'weight': 1.0}), (3685, 23236, {'weight': 1.0}), (3685, 84812, {'weight': 1.0}), (3685, 51196, {'weight': 1.0}), (3685, 1399, {'weight': 1.0}), (3685, 89869, {'weight': 1.0}), (3685, 1398, {'weight': 1.0}), (3685, 5335, {'weight': 1.0}), (3685, 5336, {'weight': 1.0}), (3685, 6714, {'weight': 1.0}), (3685, 5747, {'weight': 1.0}), (3685, 3845, {'weight': 1.0}), (8516, 9564, {'weight': 1.0}), (8516, 1399, {'weight': 1.0}), (8516, 1398, {'weight': 1.0}), (8516, 6714, {'weight': 1.0}), (8516, 5747, 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Successivamente all'interno del grafo verranno introdotte le pathway lette nel file ./data/pathways.tsv. Gli elementi che otterremo sono:
Gli ultimi due dizionari sono utili per effettuare delle conversioni.
pathways_edges = []
pathways_names = []
pathways_id = []
name2idx = {}
idx2name = {}
i = 1
nodes_list = []
with open("./data/pathways.tsv") as pathways:
pathways.readline()
for pathway in pathways:
pw = pathway.split("\t")
pw[2] = pw[2][:-1]
pw[2] = pw[2].split(";")
node_list = [(int(node)) for node in pw[2]]
for node in pw[2]:
if int(node) not in g:
g.add_node(int(node))
while i not in g:
i += 1
pathways_id.append(i)
idx2name[i] = pw[1]
name2idx[pw[1]] = i
i += 1
g.add_node(name2idx[pw[1]])
pathways_names.append(pw[1])
for n in node_list:
pathways_edges.append([pw[1], n])
g.add_edge(name2idx[pw[1]], n, weight=1.0)
g.add_edge(n, name2idx[pw[1]], weight=1.0)
pathways_names
['Oxidative phosphorylation', 'Synthesis and degradation of ketone bodies', 'Biosynthesis of unsaturated fatty acids', 'Intestinal immune network for IgA production', 'Fanconi anemia pathway', 'Wnt signaling pathway', 'Fatty acid degradation', 'Leukocyte transendothelial migration', 'Signaling pathways regulating pluripotency of stem cells', 'Glyoxylate and dicarboxylate metabolism', 'N-Glycan biosynthesis', 'Vitamin B6 metabolism', 'Various types of N-glycan biosynthesis', 'Mucin type O-glycan biosynthesis', 'Mannose type O-glycan biosynthesis', 'Amino sugar and nucleotide sugar metabolism', 'Phenylalanine, tyrosine and tryptophan biosynthesis', 'Nicotinate and nicotinamide metabolism', 'Propanoate metabolism', 'Neomycin, kanamycin and gentamicin biosynthesis', 'Natural killer cell mediated cytotoxicity', 'Fructose and mannose metabolism', 'Tight junction', 'Valine, leucine and isoleucine biosynthesis', 'Galactose metabolism', 'PPAR signaling pathway', 'Ascorbate and aldarate metabolism', 'Homologous recombination', 'Th1 and Th2 cell differentiation', 'Thiamine metabolism', 'Th17 cell differentiation', 'Aminoacyl-tRNA biosynthesis', 'IL-17 signaling pathway', 'Fatty acid biosynthesis', 'Gap junction', 'Fatty acid elongation', 'B cell receptor signaling pathway', 'Fc epsilon RI signaling pathway', 'T cell receptor signaling pathway', 'Riboflavin metabolism', 'Drug metabolism - cytochrome P450', 'Pyruvate metabolism', 'Drug metabolism - other enzymes', 'Metabolism of xenobiotics by cytochrome P450', 'Porphyrin and chlorophyll metabolism', 'Fc gamma R-mediated phagocytosis', 'Starch and sucrose metabolism', 'TNF signaling pathway', 'Phosphatidylinositol signaling system', 'Sphingolipid signaling pathway', 'Phospholipase D signaling pathway', 'Cysteine and methionine metabolism', 'Inflammatory mediator regulation of TRP channels', 'JAK-STAT signaling pathway', 'Focal adhesion', 'Pentose phosphate pathway', 'ECM-receptor interaction', 'Retinol metabolism', 'Cell adhesion molecules (CAMs)', 'Neuroactive ligand-receptor interaction', 'Pentose and glucuronate interconversions', 'Adherens junction', 'Valine, leucine and isoleucine degradation', 'Glycosphingolipid biosynthesis - lacto and neolacto series', 'Sphingolipid metabolism', 'Glycosphingolipid biosynthesis - globo and isoglobo series', 'Glycosphingolipid biosynthesis - ganglio series', 'Salivary secretion', 'Gastric acid secretion', 'Long-term depression', 'Pancreatic secretion', 'Glycolysis / Gluconeogenesis', 'Metabolic pathways', 'Alanine, aspartate and glutamate metabolism', 'Ubiquinone and other terpenoid-quinone biosynthesis', 'Renin-angiotensin system', 'Vitamin digestion and absorption', 'Mineral absorption', 'Cholesterol metabolism', 'Complement and coagulation cascades', 'Carbohydrate digestion and absorption', 'Platelet activation', 'Protein digestion and absorption', 'Antigen processing and presentation', 'Fat digestion and absorption', 'Bile secretion', 'Cytokine-cytokine receptor interaction', 'Viral protein interaction with cytokine and cytokine receptor', 'Chemokine signaling pathway', 'Tryptophan metabolism', 'Glycine, serine and threonine metabolism', 'FoxO signaling pathway', 'Olfactory transduction', 'Toll-like receptor signaling pathway', 'NF-kappa B signaling pathway', 'Steroid hormone biosynthesis', 'Citrate cycle (TCA cycle)', 'Biosynthesis of amino acids', 'HIF-1 signaling pathway', 'C-type lectin receptor signaling pathway', 'NOD-like receptor signaling pathway', 'Taste transduction', 'RIG-I-like receptor signaling pathway', 'Cytosolic DNA-sensing pathway', 'Phototransduction', 'Hippo signaling pathway', 'Vascular smooth muscle contraction', 'mTOR signaling pathway', 'Hippo signaling pathway - multiple species', 'Arachidonic acid metabolism', 'Purine metabolism', 'D-Arginine and D-ornithine metabolism', 'PI3K-Akt signaling pathway', 'AMPK signaling pathway', 'Linoleic acid metabolism', 'Tyrosine metabolism', 'D-Glutamine and D-glutamate metabolism', 'alpha-Linolenic acid metabolism', 'Circadian entrainment', 'Thermogenesis', 'Caffeine metabolism', 'Carbon metabolism', 'Nitrogen metabolism', 'Circadian rhythm', 'Glutathione metabolism', 'Aldosterone-regulated sodium reabsorption', 'Endocrine and other factor-regulated calcium reabsorption', 'Primary bile acid biosynthesis', '2-Oxocarboxylic acid metabolism', 'Phenylalanine metabolism', 'Pyrimidine metabolism', 'Glutamatergic synapse', 'Cholinergic synapse', 'Serotonergic synapse', 'Fatty acid metabolism', 'GABAergic synapse', 'Sulfur metabolism', 'Long-term potentiation', 'Vasopressin-regulated water reabsorption', 'Synaptic vesicle cycle', 'Neurotrophin signaling pathway', 'Proximal tubule bicarbonate reclamation', 'Retrograde endocannabinoid signaling', 'Dopaminergic synapse', 'VEGF signaling pathway', 'ErbB signaling pathway', 'Ras signaling pathway', 'Rap1 signaling pathway', 'Autophagy - other', 'Selenocompound metabolism', 'Apelin signaling pathway', 'Arginine and proline metabolism', 'SNARE interactions in vesicular transport', 'MAPK signaling pathway', 'Growth hormone synthesis, secretion and action', 'Mitophagy - animal', 'Regulation of actin cytoskeleton', 'Osteoclast differentiation', 'Cardiac muscle contraction', 'Endocytosis', 'cAMP signaling pathway', 'Phagosome', 'Histidine metabolism', 'Autophagy - animal', 'Adrenergic signaling in cardiomyocytes', 'Arginine biosynthesis', 'Calcium signaling pathway', 'Protein processing in endoplasmic reticulum', 'cGMP-PKG signaling pathway', 'Steroid biosynthesis', 'Terpenoid backbone biosynthesis', 'Oocyte meiosis', 'One carbon pool by folate', 'TGF-beta signaling pathway', 'Folate biosynthesis', 'Cell cycle', 'Insulin secretion', 'GnRH signaling pathway', 'Taurine and hypotaurine metabolism', 'Ovarian steroidogenesis', 'Lysine degradation', 'Progesterone-mediated oocyte maturation', 'p53 signaling pathway', 'Insulin signaling pathway', 'Thyroid hormone signaling pathway', 'Estrogen signaling pathway', 'Melanogenesis', 'Prolactin signaling pathway', 'Thyroid hormone synthesis', 'Sulfur relay system', 'Axon guidance', 'Phosphonate and phosphinate metabolism', 'Glycerolipid metabolism', 'Glycerophospholipid metabolism', 'Glucagon signaling pathway', 'Ether lipid metabolism', 'Regulation of lipolysis in adipocytes', 'Inositol phosphate metabolism', 'Renin secretion', 'Glycosylphosphatidylinositol (GPI)-anchor biosynthesis', 'Aldosterone synthesis and secretion', 'Adipocytokine signaling pathway', 'Oxytocin signaling pathway', 'Relaxin signaling pathway', 'Cortisol synthesis and secretion', 'Parathyroid hormone synthesis, secretion and action', 'Apoptosis', 'Longevity regulating pathway', 'Longevity regulating pathway - multiple species', 'Pantothenate and CoA biosynthesis', 'Notch signaling pathway', 'beta-Alanine metabolism', 'Glycosaminoglycan degradation', 'Cellular senescence', 'Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate', 'Butanoate metabolism', 'Apoptosis - multiple species', 'Ferroptosis', 'Glycosaminoglycan biosynthesis - heparan sulfate / heparin', 'Ribosome biogenesis in eukaryotes', 'Necroptosis', 'Biotin metabolism', 'RNA transport', 'Hedgehog signaling pathway', 'RNA degradation', 'Lipoic acid metabolism', 'mRNA surveillance pathway']
pathways_edges
[['Oxidative phosphorylation', 64077], ['Oxidative phosphorylation', 5464], ['Oxidative phosphorylation', 245972], ['Oxidative phosphorylation', 245973], ['Oxidative phosphorylation', 479], ['Oxidative phosphorylation', 513], ['Oxidative phosphorylation', 514], ['Oxidative phosphorylation', 515], ['Oxidative phosphorylation', 516], ['Oxidative phosphorylation', 517], ['Oxidative phosphorylation', 518], ['Oxidative phosphorylation', 155066], ['Oxidative phosphorylation', 51606], ['Oxidative phosphorylation', 9114], ['Oxidative phosphorylation', 9551], ['Oxidative phosphorylation', 9550], ['Oxidative phosphorylation', 521], ['Oxidative phosphorylation', 522], ['Oxidative phosphorylation', 523], ['Oxidative phosphorylation', 525], ['Oxidative phosphorylation', 526], ['Oxidative phosphorylation', 527], ['Oxidative phosphorylation', 528], ['Oxidative phosphorylation', 529], ['Oxidative phosphorylation', 8992], ['Oxidative phosphorylation', 90423], ['Oxidative phosphorylation', 127124], ['Oxidative phosphorylation', 23545], ['Oxidative phosphorylation', 51382], ['Oxidative phosphorylation', 495], ['Oxidative phosphorylation', 4508], ['Oxidative phosphorylation', 496], ['Oxidative phosphorylation', 4509], ['Oxidative phosphorylation', 498], ['Oxidative phosphorylation', 533], ['Oxidative phosphorylation', 534], ['Oxidative phosphorylation', 535], ['Oxidative phosphorylation', 27068], ['Oxidative phosphorylation', 537], ['Oxidative phosphorylation', 539], ['Oxidative phosphorylation', 10312], ['Oxidative phosphorylation', 10476], ['Oxidative phosphorylation', 10632], ['Oxidative phosphorylation', 50617], ['Oxidative phosphorylation', 9296], ['Oxidative phosphorylation', 506], ['Oxidative phosphorylation', 509], ['Synthesis and degradation of ketone bodies', 64064], ['Synthesis and degradation of ketone bodies', 38], ['Synthesis and degradation of ketone bodies', 39], ['Synthesis and degradation of ketone bodies', 3155], ['Synthesis and degradation of ketone bodies', 56898], ['Synthesis and degradation of ketone bodies', 54511], ['Synthesis and degradation of ketone bodies', 622], ['Synthesis and degradation of ketone bodies', 3158], ['Synthesis and degradation of ketone bodies', 3157], ['Synthesis and degradation of ketone bodies', 5019], ['Biosynthesis of unsaturated fatty acids', 641371], ['Biosynthesis of unsaturated fatty acids', 79966], ['Biosynthesis of unsaturated fatty acids', 6319], ['Biosynthesis of unsaturated fatty acids', 570], ['Biosynthesis of unsaturated fatty acids', 9415], ['Biosynthesis of unsaturated fatty acids', 3992], ['Biosynthesis of unsaturated fatty acids', 10965], ['Biosynthesis of unsaturated fatty acids', 122970], ['Biosynthesis of unsaturated fatty acids', 11332], ['Intestinal immune network for IgA production', 4055], ['Intestinal immune network for IgA production', 8174], ['Intestinal immune network for IgA production', 959], ['Intestinal immune network for IgA production', 8741], ['Intestinal immune network for IgA production', 3600], ['Intestinal immune network for IgA production', 23308], ['Intestinal immune network for IgA production', 102723407], ['Intestinal immune network for IgA production', 6370], ['Intestinal immune network for IgA production', 56477], ['Intestinal immune network for IgA production', 10673], ['Intestinal immune network for IgA production', 6387], ['Intestinal immune network for IgA production', 102723996], ['Intestinal immune network for IgA production', 941], ['Intestinal immune network for IgA production', 942], ['Intestinal immune network for IgA production', 9020], ['Intestinal immune network for IgA production', 3695], ['Intestinal immune network for IgA production', 3676], ['Intestinal immune network for IgA production', 7852], ['Intestinal immune network for IgA production', 958], ['Intestinal immune network for IgA production', 23495], ['Intestinal immune network for IgA production', 608], ['Intestinal immune network for IgA production', 3601], ['Intestinal immune network for IgA production', 29851], ['Intestinal immune network for IgA production', 5284], ['Intestinal immune network for IgA production', 10803], ['Intestinal immune network for IgA production', 2826], ['Intestinal immune network for IgA production', 115650], ['Intestinal immune network for IgA production', 940], ['Fanconi anemia pathway', 3280], ['Fanconi anemia pathway', 378708], ['Fanconi anemia pathway', 55120], ['Fanconi anemia pathway', 672], ['Fanconi anemia pathway', 84126], ['Fanconi anemia pathway', 675], ['Fanconi anemia pathway', 2189], ['Fanconi anemia pathway', 83990], ['Fanconi anemia pathway', 22909], ['Fanconi anemia pathway', 91442], ['Fanconi anemia pathway', 8940], ['Fanconi anemia pathway', 80233], ['Fanconi anemia pathway', 201254], ['Fanconi anemia pathway', 641], ['Fanconi anemia pathway', 57599], ['Fanconi anemia pathway', 79728], ['Fanconi anemia pathway', 2177], ['Fanconi anemia pathway', 2176], ['Fanconi anemia pathway', 116028], ['Fanconi anemia 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['Nicotinate and nicotinamide metabolism', 23057], ['Nicotinate and nicotinamide metabolism', 100526794], ['Nicotinate and nicotinamide metabolism', 51251], ['Nicotinate and nicotinamide metabolism', 349565], ['Nicotinate and nicotinamide metabolism', 22978], ['Nicotinate and nicotinamide metabolism', 5167], ['Nicotinate and nicotinamide metabolism', 5169], ['Nicotinate and nicotinamide metabolism', 133686], ['Nicotinate and nicotinamide metabolism', 84618], ['Nicotinate and nicotinamide metabolism', 56953], ['Nicotinate and nicotinamide metabolism', 4907], ['Nicotinate and nicotinamide metabolism', 115024], ['Nicotinate and nicotinamide metabolism', 51548], ['Nicotinate and nicotinamide metabolism', 51547], ['Nicotinate and nicotinamide metabolism', 55191], ['Nicotinate and nicotinamide metabolism', 27231], ['Nicotinate and nicotinamide metabolism', 554235], ['Nicotinate and nicotinamide metabolism', 23408], ['Nicotinate and nicotinamide metabolism', 23409], ['Nicotinate and 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['Propanoate metabolism', 1738], ['Propanoate metabolism', 51], ['Propanoate metabolism', 4329], ['Propanoate metabolism', 23417], ['Propanoate metabolism', 18], ['Propanoate metabolism', 1629], ['Propanoate metabolism', 8310], ['Propanoate metabolism', 4594], ['Propanoate metabolism', 92483], ['Propanoate metabolism', 3939], ['Propanoate metabolism', 55862], ['Propanoate metabolism', 55902], ['Propanoate metabolism', 31], ['Propanoate metabolism', 32], ['Propanoate metabolism', 5096], ['Propanoate metabolism', 35], ['Propanoate metabolism', 38], ['Propanoate metabolism', 39], ['Propanoate metabolism', 3030], ['Propanoate metabolism', 5095], ['Propanoate metabolism', 3948], ['Propanoate metabolism', 1962], ['Propanoate metabolism', 84532], ['Propanoate metabolism', 84693], ['Propanoate metabolism', 3945], ['Neomycin, kanamycin and gentamicin biosynthesis', 80201], ['Neomycin, kanamycin and gentamicin biosynthesis', 2645], ['Neomycin, kanamycin and gentamicin biosynthesis', 3101], ['Neomycin, kanamycin and gentamicin biosynthesis', 3099], ['Neomycin, kanamycin and gentamicin biosynthesis', 3098], ['Natural killer cell mediated cytotoxicity', 356], ['Natural killer cell mediated cytotoxicity', 399694], ['Natural killer cell mediated cytotoxicity', 919], ['Natural killer cell mediated cytotoxicity', 4068], ['Natural killer cell mediated cytotoxicity', 369], ['Natural killer cell mediated cytotoxicity', 2207], ['Natural killer cell mediated cytotoxicity', 10870], ['Natural killer cell mediated cytotoxicity', 5295], ['Natural killer cell mediated cytotoxicity', 5296], ['Natural killer cell mediated cytotoxicity', 5058], ['Natural killer cell mediated cytotoxicity', 5290], ['Natural killer cell mediated cytotoxicity', 5291], ['Natural killer cell mediated cytotoxicity', 5293], ['Natural killer cell mediated cytotoxicity', 5604], ['Natural killer cell mediated cytotoxicity', 5605], ['Natural killer cell mediated cytotoxicity', 7124], ['Natural killer cell mediated cytotoxicity', 3683], ['Natural killer cell mediated cytotoxicity', 4893], ['Natural killer cell mediated cytotoxicity', 4772], ['Natural killer cell mediated cytotoxicity', 4773], ['Natural killer cell mediated cytotoxicity', 3442], ['Natural killer cell mediated cytotoxicity', 3441], ['Natural killer cell mediated cytotoxicity', 3440], ['Natural killer cell mediated cytotoxicity', 3439], ['Natural killer cell mediated cytotoxicity', 27040], ['Natural killer cell mediated cytotoxicity', 3452], ['Natural killer cell mediated cytotoxicity', 3451], ['Natural killer cell mediated cytotoxicity', 3449], ['Natural killer cell mediated cytotoxicity', 3448], ['Natural killer cell mediated cytotoxicity', 3447], ['Natural killer cell mediated cytotoxicity', 3446], ['Natural killer cell mediated cytotoxicity', 962], ['Natural killer cell mediated cytotoxicity', 3445], ['Natural killer cell mediated cytotoxicity', 3444], ['Natural killer cell mediated cytotoxicity', 3443], ['Natural killer cell mediated cytotoxicity', 3689], ['Natural killer cell mediated cytotoxicity', 5880], ['Natural killer cell mediated cytotoxicity', 6850], ['Natural killer cell mediated cytotoxicity', 5881], ['Natural killer cell mediated cytotoxicity', 3460], ['Natural killer cell mediated cytotoxicity', 3459], ['Natural killer cell mediated cytotoxicity', 3458], ['Natural killer cell mediated cytotoxicity', 3456], ['Natural killer cell mediated cytotoxicity', 3455], ['Natural killer cell mediated cytotoxicity', 3454], ['Natural killer cell mediated cytotoxicity', 5879], ['Natural killer cell mediated cytotoxicity', 5530], ['Natural killer cell mediated cytotoxicity', 5894], ['Natural killer cell mediated cytotoxicity', 5532], ['Natural killer cell mediated cytotoxicity', 80329], ['Natural killer cell mediated cytotoxicity', 80328], ['Natural killer cell mediated cytotoxicity', 79465], ['Natural killer cell mediated cytotoxicity', 3107], ['Natural killer cell mediated cytotoxicity', 3106], ['Natural killer cell mediated cytotoxicity', 3105], ['Natural killer cell mediated cytotoxicity', 154064], ['Natural killer cell mediated cytotoxicity', 5781], ['Natural killer cell mediated cytotoxicity', 3002], ['Natural killer cell mediated cytotoxicity', 5533], ['Natural killer cell mediated cytotoxicity', 5534], ['Natural killer cell mediated cytotoxicity', 5535], ['Natural killer cell mediated cytotoxicity', 5777], ['Natural killer cell mediated cytotoxicity', 25759], ['Natural killer cell mediated cytotoxicity', 3133], ['Natural killer cell mediated cytotoxicity', 3803], ['Natural killer cell mediated cytotoxicity', 3804], ['Natural killer cell mediated cytotoxicity', 3805], ['Natural killer cell mediated cytotoxicity', 3802], ['Natural killer cell mediated cytotoxicity', 6654], ['Natural killer cell mediated cytotoxicity', 3265], ['Natural killer cell mediated cytotoxicity', 3384], ['Natural killer cell mediated cytotoxicity', 3383], ['Natural killer cell mediated cytotoxicity', 3937], ['Natural killer cell mediated cytotoxicity', 3135], ['Natural killer cell mediated cytotoxicity', 3811], ['Natural killer cell mediated cytotoxicity', 3932], ['Natural killer cell mediated cytotoxicity', 3812], ['Natural killer cell mediated cytotoxicity', 2185], ['Natural killer cell mediated cytotoxicity', 6655], ['Natural killer cell mediated cytotoxicity', 3821], ['Natural killer cell mediated cytotoxicity', 3824], ['Natural killer cell mediated cytotoxicity', 5582], ['Natural killer cell mediated cytotoxicity', 673], ['Natural killer cell mediated cytotoxicity', 5335], ['Natural killer cell mediated cytotoxicity', 10451], ['Natural killer cell mediated cytotoxicity', 5336], ['Natural killer cell mediated cytotoxicity', 5578], ['Natural killer cell mediated cytotoxicity', 5579], ['Natural killer cell mediated cytotoxicity', 135250], ['Natural killer cell mediated cytotoxicity', 353091], ['Natural killer cell mediated cytotoxicity', 5594], ['Natural killer cell mediated cytotoxicity', 8743], ['Natural killer cell mediated cytotoxicity', 5595], ['Natural killer cell mediated cytotoxicity', 7410], ['Natural killer cell mediated cytotoxicity', 53358], ['Natural killer cell mediated cytotoxicity', 3845], ['Natural killer cell mediated cytotoxicity', 7409], ['Natural killer cell mediated cytotoxicity', 6452], ['Natural killer cell mediated cytotoxicity', 4277], ['Natural killer cell mediated cytotoxicity', 102723407], ['Natural killer cell mediated cytotoxicity', 2885], ['Natural killer cell mediated cytotoxicity', 7535], ['Natural killer cell mediated cytotoxicity', 8503], ['Natural killer cell mediated cytotoxicity', 51744], ['Natural killer cell mediated cytotoxicity', 6464], ['Natural killer cell mediated cytotoxicity', 100507436], ['Natural killer cell mediated cytotoxicity', 57292], ['Natural killer cell mediated cytotoxicity', 2534], ['Natural killer cell mediated cytotoxicity', 7305], ['Natural killer cell mediated cytotoxicity', 355], ['Natural killer cell mediated cytotoxicity', 2215], ['Natural killer cell mediated cytotoxicity', 2214], ['Natural killer cell mediated cytotoxicity', 9437], ['Natural killer cell mediated cytotoxicity', 259197], ['Natural killer cell mediated cytotoxicity', 8795], ['Natural killer cell mediated cytotoxicity', 836], ['Natural killer cell mediated cytotoxicity', 637], ['Natural killer cell mediated cytotoxicity', 22914], ['Natural killer cell mediated cytotoxicity', 100528032], ['Natural killer cell mediated cytotoxicity', 1437], ['Natural killer cell mediated cytotoxicity', 100132285], ['Natural killer cell mediated cytotoxicity', 3806], ['Natural killer cell mediated cytotoxicity', 3808], ['Natural killer cell mediated cytotoxicity', 3809], ['Natural killer cell mediated cytotoxicity', 3810], ['Natural killer cell mediated cytotoxicity', 3822], ['Natural killer cell mediated cytotoxicity', 3823], ['Natural killer cell mediated cytotoxicity', 8797], ['Natural killer cell mediated cytotoxicity', 117157], ['Natural killer cell mediated cytotoxicity', 9436], ['Fructose and mannose metabolism', 7167], ['Fructose and mannose metabolism', 230], ['Fructose and mannose metabolism', 231], ['Fructose and mannose metabolism', 80201], ['Fructose and mannose metabolism', 57103], ['Fructose and mannose metabolism', 3795], ['Fructose and mannose metabolism', 5214], ['Fructose and mannose metabolism', 3099], ['Fructose and mannose metabolism', 26007], ['Fructose and mannose metabolism', 3098], ['Fructose and mannose metabolism', 197258], ['Fructose and mannose metabolism', 7264], ['Fructose and mannose metabolism', 4351], ['Fructose and mannose metabolism', 6652], ['Fructose and mannose metabolism', 3101], ['Fructose and mannose metabolism', 8790], ['Fructose and mannose metabolism', 29926], ['Fructose and mannose metabolism', 29925], ['Fructose and mannose metabolism', 2203], ['Fructose and mannose metabolism', 2762], ['Fructose and mannose metabolism', 8789], ['Fructose and mannose metabolism', 5372], ['Fructose and mannose metabolism', 5373], ['Fructose and mannose metabolism', 5210], ['Fructose and mannose metabolism', 5211], ['Fructose and mannose metabolism', 5213], ['Fructose and mannose metabolism', 55556], ['Fructose and mannose metabolism', 226], ['Fructose and mannose metabolism', 57016], ['Fructose and mannose metabolism', 229], ['Fructose and mannose metabolism', 5207], ['Fructose and mannose metabolism', 5208], ['Fructose and mannose metabolism', 5209], ['Tight junction', 100506658], ['Tight junction', 64398], ...]
pathways_id
[2, 25, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 48, 50, 51, 52, 54, 59, 60, 71, 90, 91, 92, 93, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 123, 124, 125, 126, 127, 128, 130, 131, 133, 134, 135, 136, 140, 142, 143, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 174, 178, 181, 182, 183, 185, 186, 187, 189, 190, 191, 196, 203, 204, 205, 207, 208, 210, 211, 212, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 226, 229, 230, 231, 239, 240, 242, 246, 247, 248, 249, 250, 251, 262, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 284, 285, 290, 291, 292, 293, 314, 316, 317, 318, 324, 329, 330, 331, 332, 335, 336, 338, 341, 344, 345, 348, 350, 353, 355, 356, 358, 359, 362, 364, 369, 374, 375, 382, 383, 384, 387, 394, 396, 397, 398, 405, 406, 408, 409, 410, 411, 412, 427, 434, 435, 438, 440, 443, 444, 445, 462, 466, 468, 471, 472, 475, 476, 477, 478, 479, 480, 481, 482, 483, 486, 487, 488, 489, 490, 491, 492, 493, 495, 496, 498, 501, 506, 509, 513, 514, 515, 516, 517, 518, 521, 522, 523, 525, 526, 527, 528, 529, 533, 534, 535, 537, 539, 545, 549, 551, 552, 553, 554]
name2idx
{'Oxidative phosphorylation': 2,
'Synthesis and degradation of ketone bodies': 25,
'Biosynthesis of unsaturated fatty acids': 27,
'Intestinal immune network for IgA production': 30,
'Fanconi anemia pathway': 31,
'Wnt signaling pathway': 32,
'Fatty acid degradation': 33,
'Leukocyte transendothelial migration': 34,
'Signaling pathways regulating pluripotency of stem cells': 35,
'Glyoxylate and dicarboxylate metabolism': 36,
'N-Glycan biosynthesis': 37,
'Vitamin B6 metabolism': 38,
'Various types of N-glycan biosynthesis': 39,
'Mucin type O-glycan biosynthesis': 48,
'Mannose type O-glycan biosynthesis': 50,
'Amino sugar and nucleotide sugar metabolism': 51,
'Phenylalanine, tyrosine and tryptophan biosynthesis': 52,
'Nicotinate and nicotinamide metabolism': 54,
'Propanoate metabolism': 59,
'Neomycin, kanamycin and gentamicin biosynthesis': 60,
'Natural killer cell mediated cytotoxicity': 71,
'Fructose and mannose metabolism': 90,
'Tight junction': 91,
'Valine, leucine and isoleucine biosynthesis': 92,
'Galactose metabolism': 93,
'PPAR signaling pathway': 107,
'Ascorbate and aldarate metabolism': 108,
'Homologous recombination': 109,
'Th1 and Th2 cell differentiation': 111,
'Thiamine metabolism': 112,
'Th17 cell differentiation': 113,
'Aminoacyl-tRNA biosynthesis': 114,
'IL-17 signaling pathway': 115,
'Fatty acid biosynthesis': 116,
'Gap junction': 117,
'Fatty acid elongation': 123,
'B cell receptor signaling pathway': 124,
'Fc epsilon RI signaling pathway': 125,
'T cell receptor signaling pathway': 126,
'Riboflavin metabolism': 127,
'Drug metabolism - cytochrome P450': 128,
'Pyruvate metabolism': 130,
'Drug metabolism - other enzymes': 131,
'Metabolism of xenobiotics by cytochrome P450': 133,
'Porphyrin and chlorophyll metabolism': 134,
'Fc gamma R-mediated phagocytosis': 135,
'Starch and sucrose metabolism': 136,
'TNF signaling pathway': 140,
'Phosphatidylinositol signaling system': 142,
'Sphingolipid signaling pathway': 143,
'Phospholipase D signaling pathway': 146,
'Cysteine and methionine metabolism': 147,
'Inflammatory mediator regulation of TRP channels': 148,
'JAK-STAT signaling pathway': 150,
'Focal adhesion': 151,
'Pentose phosphate pathway': 152,
'ECM-receptor interaction': 153,
'Retinol metabolism': 154,
'Cell adhesion molecules (CAMs)': 155,
'Neuroactive ligand-receptor interaction': 156,
'Pentose and glucuronate interconversions': 157,
'Adherens junction': 174,
'Valine, leucine and isoleucine degradation': 178,
'Glycosphingolipid biosynthesis - lacto and neolacto series': 181,
'Sphingolipid metabolism': 182,
'Glycosphingolipid biosynthesis - globo and isoglobo series': 183,
'Glycosphingolipid biosynthesis - ganglio series': 185,
'Salivary secretion': 186,
'Gastric acid secretion': 187,
'Long-term depression': 189,
'Pancreatic secretion': 190,
'Glycolysis / Gluconeogenesis': 191,
'Metabolic pathways': 196,
'Alanine, aspartate and glutamate metabolism': 203,
'Ubiquinone and other terpenoid-quinone biosynthesis': 204,
'Renin-angiotensin system': 205,
'Vitamin digestion and absorption': 207,
'Mineral absorption': 208,
'Cholesterol metabolism': 210,
'Complement and coagulation cascades': 211,
'Carbohydrate digestion and absorption': 212,
'Platelet activation': 214,
'Protein digestion and absorption': 216,
'Antigen processing and presentation': 217,
'Fat digestion and absorption': 218,
'Bile secretion': 219,
'Cytokine-cytokine receptor interaction': 220,
'Viral protein interaction with cytokine and cytokine receptor': 221,
'Chemokine signaling pathway': 222,
'Tryptophan metabolism': 223,
'Glycine, serine and threonine metabolism': 224,
'FoxO signaling pathway': 226,
'Olfactory transduction': 229,
'Toll-like receptor signaling pathway': 230,
'NF-kappa B signaling pathway': 231,
'Steroid hormone biosynthesis': 239,
'Citrate cycle (TCA cycle)': 240,
'Biosynthesis of amino acids': 242,
'HIF-1 signaling pathway': 246,
'C-type lectin receptor signaling pathway': 247,
'NOD-like receptor signaling pathway': 248,
'Taste transduction': 249,
'RIG-I-like receptor signaling pathway': 250,
'Cytosolic DNA-sensing pathway': 251,
'Phototransduction': 262,
'Hippo signaling pathway': 268,
'Vascular smooth muscle contraction': 269,
'mTOR signaling pathway': 270,
'Hippo signaling pathway - multiple species': 271,
'Arachidonic acid metabolism': 272,
'Purine metabolism': 273,
'D-Arginine and D-ornithine metabolism': 274,
'PI3K-Akt signaling pathway': 275,
'AMPK signaling pathway': 276,
'Linoleic acid metabolism': 277,
'Tyrosine metabolism': 278,
'D-Glutamine and D-glutamate metabolism': 279,
'alpha-Linolenic acid metabolism': 280,
'Circadian entrainment': 284,
'Thermogenesis': 285,
'Caffeine metabolism': 290,
'Carbon metabolism': 291,
'Nitrogen metabolism': 292,
'Circadian rhythm': 293,
'Glutathione metabolism': 314,
'Aldosterone-regulated sodium reabsorption': 316,
'Endocrine and other factor-regulated calcium reabsorption': 317,
'Primary bile acid biosynthesis': 318,
'2-Oxocarboxylic acid metabolism': 324,
'Phenylalanine metabolism': 329,
'Pyrimidine metabolism': 330,
'Glutamatergic synapse': 331,
'Cholinergic synapse': 332,
'Serotonergic synapse': 335,
'Fatty acid metabolism': 336,
'GABAergic synapse': 338,
'Sulfur metabolism': 341,
'Long-term potentiation': 344,
'Vasopressin-regulated water reabsorption': 345,
'Synaptic vesicle cycle': 348,
'Neurotrophin signaling pathway': 350,
'Proximal tubule bicarbonate reclamation': 353,
'Retrograde endocannabinoid signaling': 355,
'Dopaminergic synapse': 356,
'VEGF signaling pathway': 358,
'ErbB signaling pathway': 359,
'Ras signaling pathway': 362,
'Rap1 signaling pathway': 364,
'Autophagy - other': 369,
'Selenocompound metabolism': 374,
'Apelin signaling pathway': 375,
'Arginine and proline metabolism': 382,
'SNARE interactions in vesicular transport': 383,
'MAPK signaling pathway': 384,
'Growth hormone synthesis, secretion and action': 387,
'Mitophagy - animal': 394,
'Regulation of actin cytoskeleton': 396,
'Osteoclast differentiation': 397,
'Cardiac muscle contraction': 398,
'Endocytosis': 405,
'cAMP signaling pathway': 406,
'Phagosome': 408,
'Histidine metabolism': 409,
'Autophagy - animal': 410,
'Adrenergic signaling in cardiomyocytes': 411,
'Arginine biosynthesis': 412,
'Calcium signaling pathway': 427,
'Protein processing in endoplasmic reticulum': 434,
'cGMP-PKG signaling pathway': 435,
'Steroid biosynthesis': 438,
'Terpenoid backbone biosynthesis': 440,
'Oocyte meiosis': 443,
'One carbon pool by folate': 444,
'TGF-beta signaling pathway': 445,
'Folate biosynthesis': 462,
'Cell cycle': 466,
'Insulin secretion': 468,
'GnRH signaling pathway': 471,
'Taurine and hypotaurine metabolism': 472,
'Ovarian steroidogenesis': 475,
'Lysine degradation': 476,
'Progesterone-mediated oocyte maturation': 477,
'p53 signaling pathway': 478,
'Insulin signaling pathway': 479,
'Thyroid hormone signaling pathway': 480,
'Estrogen signaling pathway': 481,
'Melanogenesis': 482,
'Prolactin signaling pathway': 483,
'Thyroid hormone synthesis': 486,
'Sulfur relay system': 487,
'Axon guidance': 488,
'Phosphonate and phosphinate metabolism': 489,
'Glycerolipid metabolism': 490,
'Glycerophospholipid metabolism': 491,
'Glucagon signaling pathway': 492,
'Ether lipid metabolism': 493,
'Regulation of lipolysis in adipocytes': 495,
'Inositol phosphate metabolism': 496,
'Renin secretion': 498,
'Glycosylphosphatidylinositol (GPI)-anchor biosynthesis': 501,
'Aldosterone synthesis and secretion': 506,
'Adipocytokine signaling pathway': 509,
'Oxytocin signaling pathway': 513,
'Relaxin signaling pathway': 514,
'Cortisol synthesis and secretion': 515,
'Parathyroid hormone synthesis, secretion and action': 516,
'Apoptosis': 517,
'Longevity regulating pathway': 518,
'Longevity regulating pathway - multiple species': 521,
'Pantothenate and CoA biosynthesis': 522,
'Notch signaling pathway': 523,
'beta-Alanine metabolism': 525,
'Glycosaminoglycan degradation': 526,
'Cellular senescence': 527,
'Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate': 528,
'Butanoate metabolism': 529,
'Apoptosis - multiple species': 533,
'Ferroptosis': 534,
'Glycosaminoglycan biosynthesis - heparan sulfate / heparin': 535,
'Ribosome biogenesis in eukaryotes': 537,
'Necroptosis': 539,
'Biotin metabolism': 545,
'RNA transport': 549,
'Hedgehog signaling pathway': 551,
'RNA degradation': 552,
'Lipoic acid metabolism': 553,
'mRNA surveillance pathway': 554}
idx2name
{2: 'Oxidative phosphorylation',
25: 'Synthesis and degradation of ketone bodies',
27: 'Biosynthesis of unsaturated fatty acids',
30: 'Intestinal immune network for IgA production',
31: 'Fanconi anemia pathway',
32: 'Wnt signaling pathway',
33: 'Fatty acid degradation',
34: 'Leukocyte transendothelial migration',
35: 'Signaling pathways regulating pluripotency of stem cells',
36: 'Glyoxylate and dicarboxylate metabolism',
37: 'N-Glycan biosynthesis',
38: 'Vitamin B6 metabolism',
39: 'Various types of N-glycan biosynthesis',
48: 'Mucin type O-glycan biosynthesis',
50: 'Mannose type O-glycan biosynthesis',
51: 'Amino sugar and nucleotide sugar metabolism',
52: 'Phenylalanine, tyrosine and tryptophan biosynthesis',
54: 'Nicotinate and nicotinamide metabolism',
59: 'Propanoate metabolism',
60: 'Neomycin, kanamycin and gentamicin biosynthesis',
71: 'Natural killer cell mediated cytotoxicity',
90: 'Fructose and mannose metabolism',
91: 'Tight junction',
92: 'Valine, leucine and isoleucine biosynthesis',
93: 'Galactose metabolism',
107: 'PPAR signaling pathway',
108: 'Ascorbate and aldarate metabolism',
109: 'Homologous recombination',
111: 'Th1 and Th2 cell differentiation',
112: 'Thiamine metabolism',
113: 'Th17 cell differentiation',
114: 'Aminoacyl-tRNA biosynthesis',
115: 'IL-17 signaling pathway',
116: 'Fatty acid biosynthesis',
117: 'Gap junction',
123: 'Fatty acid elongation',
124: 'B cell receptor signaling pathway',
125: 'Fc epsilon RI signaling pathway',
126: 'T cell receptor signaling pathway',
127: 'Riboflavin metabolism',
128: 'Drug metabolism - cytochrome P450',
130: 'Pyruvate metabolism',
131: 'Drug metabolism - other enzymes',
133: 'Metabolism of xenobiotics by cytochrome P450',
134: 'Porphyrin and chlorophyll metabolism',
135: 'Fc gamma R-mediated phagocytosis',
136: 'Starch and sucrose metabolism',
140: 'TNF signaling pathway',
142: 'Phosphatidylinositol signaling system',
143: 'Sphingolipid signaling pathway',
146: 'Phospholipase D signaling pathway',
147: 'Cysteine and methionine metabolism',
148: 'Inflammatory mediator regulation of TRP channels',
150: 'JAK-STAT signaling pathway',
151: 'Focal adhesion',
152: 'Pentose phosphate pathway',
153: 'ECM-receptor interaction',
154: 'Retinol metabolism',
155: 'Cell adhesion molecules (CAMs)',
156: 'Neuroactive ligand-receptor interaction',
157: 'Pentose and glucuronate interconversions',
174: 'Adherens junction',
178: 'Valine, leucine and isoleucine degradation',
181: 'Glycosphingolipid biosynthesis - lacto and neolacto series',
182: 'Sphingolipid metabolism',
183: 'Glycosphingolipid biosynthesis - globo and isoglobo series',
185: 'Glycosphingolipid biosynthesis - ganglio series',
186: 'Salivary secretion',
187: 'Gastric acid secretion',
189: 'Long-term depression',
190: 'Pancreatic secretion',
191: 'Glycolysis / Gluconeogenesis',
196: 'Metabolic pathways',
203: 'Alanine, aspartate and glutamate metabolism',
204: 'Ubiquinone and other terpenoid-quinone biosynthesis',
205: 'Renin-angiotensin system',
207: 'Vitamin digestion and absorption',
208: 'Mineral absorption',
210: 'Cholesterol metabolism',
211: 'Complement and coagulation cascades',
212: 'Carbohydrate digestion and absorption',
214: 'Platelet activation',
216: 'Protein digestion and absorption',
217: 'Antigen processing and presentation',
218: 'Fat digestion and absorption',
219: 'Bile secretion',
220: 'Cytokine-cytokine receptor interaction',
221: 'Viral protein interaction with cytokine and cytokine receptor',
222: 'Chemokine signaling pathway',
223: 'Tryptophan metabolism',
224: 'Glycine, serine and threonine metabolism',
226: 'FoxO signaling pathway',
229: 'Olfactory transduction',
230: 'Toll-like receptor signaling pathway',
231: 'NF-kappa B signaling pathway',
239: 'Steroid hormone biosynthesis',
240: 'Citrate cycle (TCA cycle)',
242: 'Biosynthesis of amino acids',
246: 'HIF-1 signaling pathway',
247: 'C-type lectin receptor signaling pathway',
248: 'NOD-like receptor signaling pathway',
249: 'Taste transduction',
250: 'RIG-I-like receptor signaling pathway',
251: 'Cytosolic DNA-sensing pathway',
262: 'Phototransduction',
268: 'Hippo signaling pathway',
269: 'Vascular smooth muscle contraction',
270: 'mTOR signaling pathway',
271: 'Hippo signaling pathway - multiple species',
272: 'Arachidonic acid metabolism',
273: 'Purine metabolism',
274: 'D-Arginine and D-ornithine metabolism',
275: 'PI3K-Akt signaling pathway',
276: 'AMPK signaling pathway',
277: 'Linoleic acid metabolism',
278: 'Tyrosine metabolism',
279: 'D-Glutamine and D-glutamate metabolism',
280: 'alpha-Linolenic acid metabolism',
284: 'Circadian entrainment',
285: 'Thermogenesis',
290: 'Caffeine metabolism',
291: 'Carbon metabolism',
292: 'Nitrogen metabolism',
293: 'Circadian rhythm',
314: 'Glutathione metabolism',
316: 'Aldosterone-regulated sodium reabsorption',
317: 'Endocrine and other factor-regulated calcium reabsorption',
318: 'Primary bile acid biosynthesis',
324: '2-Oxocarboxylic acid metabolism',
329: 'Phenylalanine metabolism',
330: 'Pyrimidine metabolism',
331: 'Glutamatergic synapse',
332: 'Cholinergic synapse',
335: 'Serotonergic synapse',
336: 'Fatty acid metabolism',
338: 'GABAergic synapse',
341: 'Sulfur metabolism',
344: 'Long-term potentiation',
345: 'Vasopressin-regulated water reabsorption',
348: 'Synaptic vesicle cycle',
350: 'Neurotrophin signaling pathway',
353: 'Proximal tubule bicarbonate reclamation',
355: 'Retrograde endocannabinoid signaling',
356: 'Dopaminergic synapse',
358: 'VEGF signaling pathway',
359: 'ErbB signaling pathway',
362: 'Ras signaling pathway',
364: 'Rap1 signaling pathway',
369: 'Autophagy - other',
374: 'Selenocompound metabolism',
375: 'Apelin signaling pathway',
382: 'Arginine and proline metabolism',
383: 'SNARE interactions in vesicular transport',
384: 'MAPK signaling pathway',
387: 'Growth hormone synthesis, secretion and action',
394: 'Mitophagy - animal',
396: 'Regulation of actin cytoskeleton',
397: 'Osteoclast differentiation',
398: 'Cardiac muscle contraction',
405: 'Endocytosis',
406: 'cAMP signaling pathway',
408: 'Phagosome',
409: 'Histidine metabolism',
410: 'Autophagy - animal',
411: 'Adrenergic signaling in cardiomyocytes',
412: 'Arginine biosynthesis',
427: 'Calcium signaling pathway',
434: 'Protein processing in endoplasmic reticulum',
435: 'cGMP-PKG signaling pathway',
438: 'Steroid biosynthesis',
440: 'Terpenoid backbone biosynthesis',
443: 'Oocyte meiosis',
444: 'One carbon pool by folate',
445: 'TGF-beta signaling pathway',
462: 'Folate biosynthesis',
466: 'Cell cycle',
468: 'Insulin secretion',
471: 'GnRH signaling pathway',
472: 'Taurine and hypotaurine metabolism',
475: 'Ovarian steroidogenesis',
476: 'Lysine degradation',
477: 'Progesterone-mediated oocyte maturation',
478: 'p53 signaling pathway',
479: 'Insulin signaling pathway',
480: 'Thyroid hormone signaling pathway',
481: 'Estrogen signaling pathway',
482: 'Melanogenesis',
483: 'Prolactin signaling pathway',
486: 'Thyroid hormone synthesis',
487: 'Sulfur relay system',
488: 'Axon guidance',
489: 'Phosphonate and phosphinate metabolism',
490: 'Glycerolipid metabolism',
491: 'Glycerophospholipid metabolism',
492: 'Glucagon signaling pathway',
493: 'Ether lipid metabolism',
495: 'Regulation of lipolysis in adipocytes',
496: 'Inositol phosphate metabolism',
498: 'Renin secretion',
501: 'Glycosylphosphatidylinositol (GPI)-anchor biosynthesis',
506: 'Aldosterone synthesis and secretion',
509: 'Adipocytokine signaling pathway',
513: 'Oxytocin signaling pathway',
514: 'Relaxin signaling pathway',
515: 'Cortisol synthesis and secretion',
516: 'Parathyroid hormone synthesis, secretion and action',
517: 'Apoptosis',
518: 'Longevity regulating pathway',
521: 'Longevity regulating pathway - multiple species',
522: 'Pantothenate and CoA biosynthesis',
523: 'Notch signaling pathway',
525: 'beta-Alanine metabolism',
526: 'Glycosaminoglycan degradation',
527: 'Cellular senescence',
528: 'Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate',
529: 'Butanoate metabolism',
533: 'Apoptosis - multiple species',
534: 'Ferroptosis',
535: 'Glycosaminoglycan biosynthesis - heparan sulfate / heparin',
537: 'Ribosome biogenesis in eukaryotes',
539: 'Necroptosis',
545: 'Biotin metabolism',
549: 'RNA transport',
551: 'Hedgehog signaling pathway',
552: 'RNA degradation',
553: 'Lipoic acid metabolism',
554: 'mRNA surveillance pathway'}
A questo punto tutti i nodi vengono mappati in modo da avere dei valori che vanno da 0 a n-1, dove n è il numero dei nodi. Questo viene fatto perché semplificherà la rappresentazione della matrice di similarità tra i vari elementi.
mapping_nodes = {}
i = 0
for u in g.nodes:
mapping_nodes[u] = i
i += 1
mapping_nodes
{3640: 0,
51289: 1,
122042: 2,
339403: 3,
59350: 4,
284217: 5,
3680: 6,
3696: 7,
3674: 8,
3675: 9,
3676: 10,
3655: 11,
3678: 12,
3679: 13,
22987: 14,
22801: 15,
3690: 16,
3691: 17,
3693: 18,
9899: 19,
3694: 20,
3672: 21,
3695: 22,
3673: 23,
960: 24,
3685: 25,
8516: 26,
9900: 27,
3688: 28,
8515: 29,
1605: 30,
5747: 31,
121275: 32,
2788: 33,
2774: 34,
2782: 35,
51764: 36,
3630: 37,
4233: 38,
4893: 39,
3265: 40,
8471: 41,
3480: 42,
4804: 43,
3815: 44,
1436: 45,
2324: 46,
2322: 47,
2321: 48,
5159: 49,
22808: 50,
1956: 51,
22800: 52,
7010: 53,
8660: 54,
3791: 55,
5156: 56,
2066: 57,
2264: 58,
2065: 59,
2263: 60,
2064: 61,
2261: 62,
2260: 63,
4914: 64,
4915: 65,
6237: 66,
3643: 67,
1969: 68,
3645: 69,
3667: 70,
3845: 71,
2309: 72,
114907: 73,
10370: 74,
8698: 75,
1263: 76,
2592: 77,
9140: 78,
472: 79,
595: 80,
10733: 81,
10018: 82,
85417: 83,
356: 84,
1410: 85,
3312: 86,
5896: 87,
5897: 88,
5934: 89,
11345: 90,
9474: 91,
8743: 92,
92579: 93,
1032: 94,
1030: 95,
1027: 96,
1026: 97,
5347: 98,
5105: 99,
604: 100,
5106: 101,
847: 102,
1901: 103,
4616: 104,
891: 105,
10912: 106,
894: 107,
3575: 108,
6647: 109,
6648: 110,
9133: 111,
3310: 112,
23710: 113,
26260: 114,
3306: 115,
10769: 116,
3305: 117,
3304: 118,
664: 119,
3303: 120,
57818: 121,
901: 122,
10365: 123,
11337: 124,
1647: 125,
2538: 126,
2308: 127,
126129: 128,
1375: 129,
2203: 130,
8789: 131,
1374: 132,
4982: 133,
8600: 134,
3651: 135,
2: 136,
5624: 137,
55578: 138,
285973: 139,
79065: 140,
5781: 141,
2885: 142,
1399: 143,
1398: 144,
57104: 145,
8503: 146,
399694: 147,
11145: 148,
2549: 149,
25759: 150,
5295: 151,
5296: 152,
5330: 153,
5331: 154,
6464: 155,
5332: 156,
5290: 157,
23236: 158,
5291: 159,
5293: 160,
10603: 161,
867: 162,
53358: 163,
868: 164,
9846: 165,
5604: 166,
5605: 167,
6654: 168,
6655: 169,
4991: 170,
4992: 171,
3661: 172,
6373: 173,
3442: 174,
3441: 175,
3440: 176,
338376: 177,
3439: 178,
56832: 179,
3456: 180,
958: 181,
4283: 182,
3452: 183,
3451: 184,
3449: 185,
3448: 186,
3447: 187,
3446: 188,
3445: 189,
3467: 190,
941: 191,
3444: 192,
942: 193,
3443: 194,
3627: 195,
4993: 196,
1000: 197,
2331: 198,
7043: 199,
7040: 200,
7042: 201,
2323: 202,
4985: 203,
2773: 204,
2771: 205,
2770: 206,
3654: 207,
7189: 208,
6885: 209,
3551: 210,
3665: 211,
257397: 212,
10454: 213,
23118: 214,
9564: 215,
6714: 216,
3656: 217,
4988: 218,
2775: 219,
3659: 220,
3593: 221,
3592: 222,
55593: 223,
7187: 224,
81858: 225,
8737: 226,
8767: 227,
79541: 228,
79544: 229,
2335: 230,
3681: 231,
3682: 232,
3683: 233,
3684: 234,
6385: 235,
6382: 236,
3687: 237,
3689: 238,
1002: 239,
4994: 240,
3663: 241,
3569: 242,
6352: 243,
414062: 244,
7124: 245,
3576: 246,
3553: 247,
6348: 248,
6349: 249,
4995: 250,
79549: 251,
5294: 252,
146850: 253,
23533: 254,
7412: 255,
7410: 256,
3385: 257,
2185: 258,
3384: 259,
3383: 260,
10451: 261,
10666: 262,
7409: 263,
2353: 264,
6351: 265,
4772: 266,
2625: 267,
1019: 268,
3559: 269,
3558: 270,
355: 271,
799: 272,
54: 273,
3567: 274,
3566: 275,
3565: 276,
8739: 277,
9560: 278,
388372: 279,
1437: 280,
1513: 281,
2689: 282,
3458: 283,
2688: 284,
30009: 285,
7157: 286,
3596: 287,
3595: 288,
3594: 289,
1443: 290,
1442: 291,
3586: 292,
1022: 293,
1017: 294,
983: 295,
1021: 296,
5933: 297,
5925: 298,
1020: 299,
1808: 300,
5111: 301,
861: 302,
25847: 303,
8697: 304,
10393: 305,
29945: 306,
29882: 307,
990: 308,
995: 309,
996: 310,
1871: 311,
1870: 312,
4303: 313,
4605: 314,
51529: 315,
64682: 316,
8881: 317,
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1028: 320,
51434: 321,
51433: 322,
1869: 323,
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5335: 325,
5336: 326,
113026: 327,
5333: 328,
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51196: 330,
89869: 331,
896: 332,
1031: 333,
1029: 334,
4193: 335,
8900: 336,
890: 337,
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898: 339,
2357: 340,
2778: 341,
2776: 342,
2355: 343,
2354: 344,
59082: 345,
834: 346,
255738: 347,
3949: 348,
1075: 349,
330: 350,
331: 351,
596: 352,
332: 353,
598: 354,
329: 355,
637: 356,
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85366: 358,
10627: 359,
58498: 360,
29895: 361,
140465: 362,
93408: 363,
10398: 364,
4633: 365,
4634: 366,
4635: 367,
103910: 368,
4636: 369,
4637: 370,
1081: 371,
7253: 372,
4881: 373,
7434: 374,
3362: 375,
2492: 376,
3360: 377,
153: 378,
135: 379,
2696: 380,
2740: 381,
117: 382,
4158: 383,
5732: 384,
3973: 385,
1816: 386,
139760: 387,
1812: 388,
440275: 389,
1965: 390,
4780: 391,
9466: 392,
4352: 393,
149233: 394,
3563: 395,
3561: 396,
9180: 397,
3560: 398,
2690: 399,
3460: 400,
3581: 401,
5618: 402,
3459: 403,
116379: 404,
3455: 405,
3598: 406,
3454: 407,
3597: 408,
3953: 409,
1439: 410,
3977: 411,
50615: 412,
1438: 413,
163702: 414,
3572: 415,
1271: 416,
3570: 417,
64109: 418,
3590: 419,
3568: 420,
3601: 421,
3588: 422,
3587: 423,
58985: 424,
1441: 425,
2057: 426,
53833: 427,
53832: 428,
403282: 429,
403284: 430,
255725: 431,
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9821: 433,
89849: 434,
55054: 435,
55534: 436,
11317: 437,
3516: 438,
9825: 439,
1540: 440,
207: 441,
9586: 442,
5140: 443,
6199: 444,
6198: 445,
7248: 446,
1385: 447,
3164: 448,
111: 449,
112: 450,
113: 451,
114: 452,
115: 453,
4842: 454,
4843: 455,
4846: 456,
90673: 457,
5594: 458,
5595: 459,
90993: 460,
64764: 461,
5509: 462,
1147: 463,
1388: 464,
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51256: 466,
842: 467,
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1386: 470,
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5500: 473,
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5501: 475,
4217: 476,
6517: 477,
5506: 478,
6518: 479,
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5563: 487,
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572: 491,
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107: 504,
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108: 506,
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109: 508,
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387: 512,
208: 513,
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317: 515,
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273: 530,
274: 531,
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476: 533,
477: 534,
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482: 539,
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483: 542,
486: 543,
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3937: 547,
695: 548,
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23439: 550,
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10000: 552,
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998: 555,
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9630: 565,
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5728: 569,
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1432: 581,
5599: 582,
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5600: 584,
5601: 585,
5602: 586,
6833: 587,
5603: 588,
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8536: 590,
466: 591,
7220: 592,
659: 593,
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3315: 595,
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8556: 597,
51343: 598,
7224: 599,
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8554: 601,
6773: 602,
6772: 603,
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6774: 605,
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6778: 608,
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8555: 610,
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545: 612,
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23035: 617,
268: 618,
269: 619,
657: 620,
658: 621,
343169: 622,
11059: 623,
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253314: 630,
55845: 631,
8936: 632,
9470: 633,
1977: 634,
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284: 637,
285: 638,
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29883: 668,
255967: 669,
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632: 698,
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909: 700,
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7976: 730,
11211: 731,
1101: 732,
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57506: 734,
1111: 735,
993: 736,
994: 737,
3776: 738,
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5261: 768,
808: 769,
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801: 780,
805: 781,
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8620: 865,
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2833: 872,
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643: 880,
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26060: 893,
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90: 896,
91: 897,
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3875: 982,
3857: 983,
5914: 984,
8688: 985,
8689: 986,
7039: 987,
8687: 988,
147183: 989,
7031: 990,
192666: 991,
100653049: 992,
3861: 993,
3883: 994,
3884: 995,
342574: 996,
3885: 997,
1509: 998,
3886: 999,
...}
real_nodes = {v: k for k,v in mapping_nodes.items()}
real_nodes
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992: 100653049,
993: 3861,
994: 3883,
995: 3884,
996: 342574,
997: 3885,
998: 1509,
999: 3886,
...}
Viene creato un grafo che mantiene gli edges precedenti, ma dove ogni nodo ha come id quello del mappping.
with open("./data/map_graph.tsv", "w") as fg:
for u,v,d in g.edges(data=True):
fg.write(str(mapping_nodes[u]) + "\t" + str(mapping_nodes[v]) + "\t" + str(int(d["weight"])) + "\n")
g = nx.read_edgelist('./data/map_graph.tsv', nodetype=int,
data = (('weight',float),), create_using=nx.DiGraph())
print(g.edges(data=True))
[(0, 1, {'weight': 1.0}), (0, 2, {'weight': 1.0}), (0, 3, {'weight': 1.0}), (0, 4, {'weight': 1.0}), (0, 2419, {'weight': 1.0}), (0, 3503, {'weight': 1.0}), (1, 51, {'weight': 1.0}), (1, 2419, {'weight': 1.0}), (1, 3503, {'weight': 1.0}), (2, 2419, {'weight': 1.0}), (2, 3503, {'weight': 1.0}), (3, 2419, {'weight': 1.0}), (3, 3503, {'weight': 1.0}), (4, 2419, {'weight': 1.0}), (4, 3503, {'weight': 1.0}), (2419, 1309, {'weight': 1.0}), (2419, 1310, {'weight': 1.0}), (2419, 1311, {'weight': 1.0}), (2419, 32, {'weight': 1.0}), (2419, 1312, {'weight': 1.0}), (2419, 868, {'weight': 1.0}), (2419, 1313, {'weight': 1.0}), (2419, 870, {'weight': 1.0}), (2419, 1314, {'weight': 1.0}), (2419, 1315, {'weight': 1.0}), (2419, 1316, {'weight': 1.0}), (2419, 1317, {'weight': 1.0}), (2419, 1318, {'weight': 1.0}), (2419, 1319, {'weight': 1.0}), (2419, 1320, {'weight': 1.0}), (2419, 884, {'weight': 1.0}), (2419, 170, {'weight': 1.0}), (2419, 171, {'weight': 1.0}), (2419, 196, {'weight': 1.0}), (2419, 1321, 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nx.adjacency_matrix(g, nodelist=list(real_nodes.keys())).todense()
matrix([[0., 1., 1., ..., 0., 0., 0.],
[0., 0., 0., ..., 0., 0., 0.],
[0., 0., 0., ..., 0., 0., 0.],
...,
[0., 0., 0., ..., 0., 0., 0.],
[0., 0., 0., ..., 0., 0., 0.],
[0., 0., 0., ..., 0., 0., 0.]])
W = nx.adjacency_matrix(g, nodelist=list(real_nodes.keys()))
C = normalize(W, norm='l1', axis=0)
C = np.sqrt(c) * C
mmwrite("./data/graph.mtx", nx.adjacency_matrix(g, nodelist=list(real_nodes.keys())))
c = 0.6
num_iter = 5
rank = 1
oversampl = 0.0001
U_file = "./data/U_graph.csv"
d_file = "./data/d_graph.csv"
graph_filename_mtx = "./data/graph.mtx"
!./simrank_lowrank/build/simrank_lowrank -g $graph_filename_mtx -i $num_iter -c $c -r $rank -s $oversampl -u $U_file -d $d_file
Reading graph from ./data/graph.mtx... Number of vertices = 5476 Number of edges = 63670 Reading graph from ./data/graph.mtx...Done Compute low rank approximation of SimRank... Iteration 1 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 2 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 3 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 4 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Iteration 5 SVD... QR... QR...Done Eigen decomposition... Eigen decomposition...Done SVD...Done Compute low rank approximation of SimRank... Done Saving lowrank matrices... Saving lowrank matrices...Done Elapsed time = 49.913938
U = read_csv("./data/U_graph.csv", header=None)
d = np.array(read_csv("./data/d_graph.csv", header=None))
D = np.diag(d[:, 0])
CTC = C.T.dot(C)
S_appr = np.eye(C.shape[0]) + CTC - np.diag(CTC.diagonal()) + U.dot(D).dot(U.T)
S_appr
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... | 5466 | 5467 | 5468 | 5469 | 5470 | 5471 | 5472 | 5473 | 5474 | 5475 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.015901 | 0.109284 | 0.105180 | 0.099453 | 0.115148 | 0.016983 | 0.016407 | 0.013853 | 0.007875 | 0.014899 | ... | 0.029143 | 0.025498 | 0.019182 | 0.014725 | 0.023054 | 0.020137 | 0.015706 | 0.021011 | 0.019811 | 0.017449 |
| 1 | 0.109284 | 1.034936 | 0.114568 | 0.106079 | 0.129343 | 0.025174 | 0.024320 | 0.020534 | 0.011673 | 0.022085 | ... | 0.043198 | 0.037794 | 0.028433 | 0.021827 | 0.034172 | 0.029848 | 0.023280 | 0.031145 | 0.029365 | 0.025865 |
| 2 | 0.105180 | 0.114568 | 1.023830 | 0.102533 | 0.121747 | 0.020791 | 0.020086 | 0.016959 | 0.009641 | 0.018240 | ... | 0.035677 | 0.031214 | 0.023483 | 0.018027 | 0.028223 | 0.024651 | 0.019227 | 0.025722 | 0.024252 | 0.021361 |
| 3 | 0.099453 | 0.106079 | 0.102533 | 1.011871 | 0.111146 | 0.014674 | 0.014177 | 0.011970 | 0.006804 | 0.012873 | ... | 0.025180 | 0.022031 | 0.016574 | 0.012723 | 0.019919 | 0.017399 | 0.013570 | 0.018154 | 0.017117 | 0.015077 |
| 4 | 0.115148 | 0.129343 | 0.121747 | 0.111146 | 1.054485 | 0.031438 | 0.030372 | 0.025644 | 0.014578 | 0.027580 | ... | 0.053946 | 0.047198 | 0.035508 | 0.027258 | 0.042675 | 0.037275 | 0.029073 | 0.038894 | 0.036671 | 0.032300 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 5471 | 0.020137 | 0.029848 | 0.024651 | 0.017399 | 0.037275 | 0.021508 | 0.020778 | 0.017544 | 0.009973 | 0.018868 | ... | 0.636907 | 0.632290 | 0.624292 | 0.618648 | 0.629195 | 1.025501 | 0.619890 | 0.626609 | 0.625088 | 0.622098 |
| 5472 | 0.015706 | 0.023280 | 0.019227 | 0.013570 | 0.029073 | 0.016775 | 0.016206 | 0.013683 | 0.007779 | 0.014716 | ... | 0.628785 | 0.625185 | 0.618947 | 0.614545 | 0.622771 | 0.619890 | 1.015513 | 0.620753 | 0.619568 | 0.617235 |
| 5473 | 0.021011 | 0.031145 | 0.025722 | 0.018154 | 0.038894 | 0.022442 | 0.021681 | 0.018306 | 0.010406 | 0.019688 | ... | 0.638509 | 0.633692 | 0.625347 | 0.619458 | 0.630463 | 0.626609 | 0.620753 | 1.027764 | 0.626178 | 0.623057 |
| 5474 | 0.019811 | 0.029365 | 0.024252 | 0.017117 | 0.036671 | 0.021159 | 0.020442 | 0.017260 | 0.009812 | 0.018563 | ... | 0.636309 | 0.631767 | 0.623899 | 0.618346 | 0.628723 | 0.625088 | 0.619568 | 0.626178 | 1.024682 | 0.621740 |
| 5475 | 0.017449 | 0.025865 | 0.021361 | 0.015077 | 0.032300 | 0.018637 | 0.018005 | 0.015202 | 0.008642 | 0.016350 | ... | 0.631981 | 0.627981 | 0.621050 | 0.616159 | 0.625299 | 0.622098 | 0.617235 | 0.623057 | 0.621740 | 1.019149 |
5476 rows × 5476 columns
Per eseguire il SimRank con networkx è possibile utilizzare le righe di codice sotto, basta levare i commenti. Il processo impiegherà un po' di tempo, proprio per questo motivo il risultato è stato già ottenuto e salvato su un file csv e su un json.
#sim = nx.simrank_similarity(g, importance_factor=0.6, max_iterations=5, tolerance=0.0001)
#r = [[sim[u][v] for v in sorted(sim[u])] for u in sorted(sim)]
#sim_array = array(r)
#df = pd.DataFrame(sim_array, columns=range(len(g.nodes)))
#import json
#with open('./data/simrank.json', 'w') as fp:
# json.dump(sim, fp)
#df.to_csv("./data/simrank.csv", index=False)
df = read_csv("./data/simrank.csv")
df
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... | 5466 | 5467 | 5468 | 5469 | 5470 | 5471 | 5472 | 5473 | 5474 | 5475 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.000000 | 0.088520 | 0.088520 | 0.088520 | 0.088520 | 0.001939 | 0.001191 | 0.001208 | 0.001197 | 0.001208 | ... | 0.000775 | 0.000775 | 0.000775 | 0.000775 | 0.000775 | 0.000775 | 0.000775 | 0.000775 | 0.000775 | 0.000775 |
| 1 | 0.088520 | 1.000000 | 0.161040 | 0.161040 | 0.161040 | 0.001719 | 0.005027 | 0.005102 | 0.004570 | 0.005102 | ... | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 |
| 2 | 0.088520 | 0.161040 | 1.000000 | 0.161040 | 0.161040 | 0.001719 | 0.005027 | 0.005102 | 0.004570 | 0.005102 | ... | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 |
| 3 | 0.088520 | 0.161040 | 0.161040 | 1.000000 | 0.161040 | 0.001719 | 0.005027 | 0.005102 | 0.004570 | 0.005102 | ... | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 |
| 4 | 0.088520 | 0.161040 | 0.161040 | 0.161040 | 1.000000 | 0.001719 | 0.005027 | 0.005102 | 0.004570 | 0.005102 | ... | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.002416 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 5471 | 0.000775 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.001404 | 0.000362 | 0.000362 | 0.000369 | 0.000362 | ... | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 1.000000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 |
| 5472 | 0.000775 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.001404 | 0.000362 | 0.000362 | 0.000369 | 0.000362 | ... | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 1.000000 | 0.600000 | 0.600000 | 0.600000 |
| 5473 | 0.000775 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.001404 | 0.000362 | 0.000362 | 0.000369 | 0.000362 | ... | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 1.000000 | 0.600000 | 0.600000 |
| 5474 | 0.000775 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.001404 | 0.000362 | 0.000362 | 0.000369 | 0.000362 | ... | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 1.000000 | 0.600000 |
| 5475 | 0.000775 | 0.002416 | 0.002416 | 0.002416 | 0.002416 | 0.001404 | 0.000362 | 0.000362 | 0.000369 | 0.000362 | ... | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 0.600000 | 1.000000 |
5476 rows × 5476 columns
print("Difference in Frobenius norm =", np.linalg.norm(S_appr.to_numpy() - df.to_numpy()) / np.linalg.norm(df.to_numpy()))
Difference in Frobenius norm = 0.3741417259611122
Il risultato sopra restituisce la differenza come norma di Frobenius tra il SimRank calcolato da networkx e quello approssimato dal SimRank-lowrank. Quello che osserviamo è che il risultato è accettabile, quindi se non si vuole perdere molto trempo la scelta migliore è il SimRank-lowrank.
A questo punto possiamo rappresentare visivamente le similarità tra le pathway biologiche all'interno del grafo considerato.
Prima bisogna effettuare un mapping tra i nomi delle pathway e gli id del grafo.
pathway_names_id = {}
for key, value in idx2name.items():
pathway_names_id[mapping_nodes[key]] = value
pathway_names_id
{136: 'Oxidative phosphorylation',
1064: 'Synthesis and degradation of ketone bodies',
1892: 'Biosynthesis of unsaturated fatty acids',
2067: 'Intestinal immune network for IgA production',
2676: 'Fanconi anemia pathway',
2677: 'Wnt signaling pathway',
2071: 'Fatty acid degradation',
2072: 'Leukocyte transendothelial migration',
3586: 'Signaling pathways regulating pluripotency of stem cells',
3587: 'Glyoxylate and dicarboxylate metabolism',
3588: 'N-Glycan biosynthesis',
3533: 'Vitamin B6 metabolism',
3534: 'Various types of N-glycan biosynthesis',
3604: 'Mucin type O-glycan biosynthesis',
3608: 'Mannose type O-glycan biosynthesis',
2040: 'Amino sugar and nucleotide sugar metabolism',
1107: 'Phenylalanine, tyrosine and tryptophan biosynthesis',
273: 'Nicotinate and nicotinamide metabolism',
2650: 'Propanoate metabolism',
1091: 'Neomycin, kanamycin and gentamicin biosynthesis',
1086: 'Natural killer cell mediated cytotoxicity',
896: 'Fructose and mannose metabolism',
897: 'Tight junction',
1136: 'Valine, leucine and isoleucine biosynthesis',
1137: 'Galactose metabolism',
504: 'PPAR signaling pathway',
506: 'Ascorbate and aldarate metabolism',
508: 'Homologous recombination',
449: 'Th1 and Th2 cell differentiation',
450: 'Thiamine metabolism',
451: 'Th17 cell differentiation',
452: 'Aminoacyl-tRNA biosynthesis',
453: 'IL-17 signaling pathway',
3419: 'Fatty acid biosynthesis',
382: 'Gap junction',
2050: 'Fatty acid elongation',
3575: 'B cell receptor signaling pathway',
3576: 'Fc epsilon RI signaling pathway',
3577: 'T cell receptor signaling pathway',
3578: 'Riboflavin metabolism',
3579: 'Drug metabolism - cytochrome P450',
3581: 'Pyruvate metabolism',
3582: 'Drug metabolism - other enzymes',
3428: 'Metabolism of xenobiotics by cytochrome P450',
1170: 'Porphyrin and chlorophyll metabolism',
379: 'Fc gamma R-mediated phagocytosis',
3429: 'Starch and sucrose metabolism',
1172: 'TNF signaling pathway',
2485: 'Phosphatidylinositol signaling system',
2487: 'Sphingolipid signaling pathway',
3431: 'Phospholipase D signaling pathway',
3432: 'Cysteine and methionine metabolism',
3433: 'Inflammatory mediator regulation of TRP channels',
3439: 'JAK-STAT signaling pathway',
3440: 'Focal adhesion',
3441: 'Pentose phosphate pathway',
378: 'ECM-receptor interaction',
2224: 'Retinol metabolism',
3442: 'Cell adhesion molecules (CAMs)',
2419: 'Neuroactive ligand-receptor interaction',
2420: 'Pentose and glucuronate interconversions',
1746: 'Adherens junction',
4156: 'Valine, leucine and isoleucine degradation',
2682: 'Glycosphingolipid biosynthesis - lacto and neolacto series',
2977: 'Sphingolipid metabolism',
3469: 'Glycosphingolipid biosynthesis - globo and isoglobo series',
1979: 'Glycosphingolipid biosynthesis - ganglio series',
3471: 'Salivary secretion',
1999: 'Gastric acid secretion',
3624: 'Long-term depression',
3474: 'Pancreatic secretion',
4218: 'Glycolysis / Gluconeogenesis',
3476: 'Metabolic pathways',
3911: 'Alanine, aspartate and glutamate metabolism',
3912: 'Ubiquinone and other terpenoid-quinone biosynthesis',
3915: 'Renin-angiotensin system',
441: 'Vitamin digestion and absorption',
513: 'Mineral absorption',
4135: 'Cholesterol metabolism',
4136: 'Complement and coagulation cascades',
4137: 'Carbohydrate digestion and absorption',
4323: 'Platelet activation',
4301: 'Protein digestion and absorption',
3584: 'Antigen processing and presentation',
4056: 'Fat digestion and absorption',
3585: 'Bile secretion',
4059: 'Cytokine-cytokine receptor interaction',
4060: 'Viral protein interaction with cytokine and cytokine receptor',
4061: 'Chemokine signaling pathway',
3593: 'Tryptophan metabolism',
3594: 'Glycine, serine and threonine metabolism',
1296: 'FoxO signaling pathway',
1297: 'Olfactory transduction',
1268: 'Toll-like receptor signaling pathway',
3834: 'NF-kappa B signaling pathway',
4556: 'Steroid hormone biosynthesis',
4561: 'Citrate cycle (TCA cycle)',
4562: 'Biosynthesis of amino acids',
2201: 'HIF-1 signaling pathway',
4564: 'C-type lectin receptor signaling pathway',
3914: 'NOD-like receptor signaling pathway',
3916: 'Taste transduction',
3904: 'RIG-I-like receptor signaling pathway',
3905: 'Cytosolic DNA-sensing pathway',
4228: 'Phototransduction',
618: 'Hippo signaling pathway',
619: 'Vascular smooth muscle contraction',
4578: 'mTOR signaling pathway',
4580: 'Hippo signaling pathway - multiple species',
4582: 'Arachidonic acid metabolism',
530: 'Purine metabolism',
531: 'D-Arginine and D-ornithine metabolism',
3607: 'PI3K-Akt signaling pathway',
4149: 'AMPK signaling pathway',
4150: 'Linoleic acid metabolism',
4151: 'Tyrosine metabolism',
4152: 'D-Glutamine and D-glutamate metabolism',
4153: 'alpha-Linolenic acid metabolism',
637: 'Circadian entrainment',
638: 'Thermogenesis',
4588: 'Caffeine metabolism',
1713: 'Carbon metabolism',
1714: 'Nitrogen metabolism',
1715: 'Circadian rhythm',
4680: 'Glutathione metabolism',
2749: 'Aldosterone-regulated sodium reabsorption',
515: 'Endocrine and other factor-regulated calcium reabsorption',
4681: 'Primary bile acid biosynthesis',
886: '2-Oxocarboxylic acid metabolism',
355: 'Phenylalanine metabolism',
350: 'Pyrimidine metabolism',
351: 'Glutamatergic synapse',
353: 'Cholinergic synapse',
920: 'Serotonergic synapse',
2063: 'Fatty acid metabolism',
4996: 'GABAergic synapse',
937: 'Sulfur metabolism',
939: 'Long-term potentiation',
2082: 'Vasopressin-regulated water reabsorption',
4998: 'Synaptic vesicle cycle',
960: 'Neurotrophin signaling pathway',
4705: 'Proximal tubule bicarbonate reclamation',
271: 'Retrograde endocannabinoid signaling',
84: 'Dopaminergic synapse',
964: 'VEGF signaling pathway',
1882: 'ErbB signaling pathway',
4476: 'Ras signaling pathway',
2047: 'Rap1 signaling pathway',
1048: 'Autophagy - other',
1071: 'Selenocompound metabolism',
1072: 'Apelin signaling pathway',
820: 'Arginine and proline metabolism',
4719: 'SNARE interactions in vesicular transport',
4720: 'MAPK signaling pathway',
512: 'Growth hormone synthesis, secretion and action',
1097: 'Mitophagy - animal',
1098: 'Regulation of actin cytoskeleton',
1099: 'Osteoclast differentiation',
1100: 'Cardiac muscle contraction',
1264: 'Endocytosis',
1301: 'cAMP signaling pathway',
1308: 'Phagosome',
1660: 'Histidine metabolism',
4444: 'Autophagy - animal',
4808: 'Adrenergic signaling in cardiomyocytes',
5019: 'Arginine biosynthesis',
4460: 'Calcium signaling pathway',
1681: 'Protein processing in endoplasmic reticulum',
4818: 'cGMP-PKG signaling pathway',
4819: 'Steroid biosynthesis',
4821: 'Terpenoid backbone biosynthesis',
4822: 'Oocyte meiosis',
5144: 'One carbon pool by folate',
4823: 'TGF-beta signaling pathway',
1753: 'Folate biosynthesis',
591: 'Cell cycle',
502: 'Insulin secretion',
4829: 'GnRH signaling pathway',
79: 'Taurine and hypotaurine metabolism',
4991: 'Ovarian steroidogenesis',
533: 'Lysine degradation',
534: 'Progesterone-mediated oocyte maturation',
535: 'p53 signaling pathway',
3501: 'Insulin signaling pathway',
537: 'Thyroid hormone signaling pathway',
538: 'Estrogen signaling pathway',
539: 'Melanogenesis',
542: 'Prolactin signaling pathway',
543: 'Thyroid hormone synthesis',
2611: 'Sulfur relay system',
2612: 'Axon guidance',
2613: 'Phosphonate and phosphinate metabolism',
1726: 'Glycerolipid metabolism',
1727: 'Glycerophospholipid metabolism',
1728: 'Glucagon signaling pathway',
1730: 'Ether lipid metabolism',
3516: 'Regulation of lipolysis in adipocytes',
3518: 'Inositol phosphate metabolism',
3520: 'Renin secretion',
3595: 'Glycosylphosphatidylinositol (GPI)-anchor biosynthesis',
3530: 'Aldosterone synthesis and secretion',
3531: 'Adipocytokine signaling pathway',
3502: 'Oxytocin signaling pathway',
3503: 'Relaxin signaling pathway',
3504: 'Cortisol synthesis and secretion',
3505: 'Parathyroid hormone synthesis, secretion and action',
3506: 'Apoptosis',
3507: 'Longevity regulating pathway',
3511: 'Longevity regulating pathway - multiple species',
3512: 'Pantothenate and CoA biosynthesis',
1927: 'Notch signaling pathway',
1933: 'beta-Alanine metabolism',
1934: 'Glycosaminoglycan degradation',
3513: 'Cellular senescence',
1935: 'Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate',
1936: 'Butanoate metabolism',
3521: 'Apoptosis - multiple species',
1939: 'Ferroptosis',
3522: 'Glycosaminoglycan biosynthesis - heparan sulfate / heparin',
3524: 'Ribosome biogenesis in eukaryotes',
3525: 'Necroptosis',
612: 'Biotin metabolism',
4403: 'RNA transport',
1974: 'Hedgehog signaling pathway',
1981: 'RNA degradation',
1983: 'Lipoic acid metabolism',
1984: 'mRNA surveillance pathway'}
pathway_id_name = {v: k for k,v in pathway_names_id.items()}
pathway_id_name
{'Oxidative phosphorylation': 136,
'Synthesis and degradation of ketone bodies': 1064,
'Biosynthesis of unsaturated fatty acids': 1892,
'Intestinal immune network for IgA production': 2067,
'Fanconi anemia pathway': 2676,
'Wnt signaling pathway': 2677,
'Fatty acid degradation': 2071,
'Leukocyte transendothelial migration': 2072,
'Signaling pathways regulating pluripotency of stem cells': 3586,
'Glyoxylate and dicarboxylate metabolism': 3587,
'N-Glycan biosynthesis': 3588,
'Vitamin B6 metabolism': 3533,
'Various types of N-glycan biosynthesis': 3534,
'Mucin type O-glycan biosynthesis': 3604,
'Mannose type O-glycan biosynthesis': 3608,
'Amino sugar and nucleotide sugar metabolism': 2040,
'Phenylalanine, tyrosine and tryptophan biosynthesis': 1107,
'Nicotinate and nicotinamide metabolism': 273,
'Propanoate metabolism': 2650,
'Neomycin, kanamycin and gentamicin biosynthesis': 1091,
'Natural killer cell mediated cytotoxicity': 1086,
'Fructose and mannose metabolism': 896,
'Tight junction': 897,
'Valine, leucine and isoleucine biosynthesis': 1136,
'Galactose metabolism': 1137,
'PPAR signaling pathway': 504,
'Ascorbate and aldarate metabolism': 506,
'Homologous recombination': 508,
'Th1 and Th2 cell differentiation': 449,
'Thiamine metabolism': 450,
'Th17 cell differentiation': 451,
'Aminoacyl-tRNA biosynthesis': 452,
'IL-17 signaling pathway': 453,
'Fatty acid biosynthesis': 3419,
'Gap junction': 382,
'Fatty acid elongation': 2050,
'B cell receptor signaling pathway': 3575,
'Fc epsilon RI signaling pathway': 3576,
'T cell receptor signaling pathway': 3577,
'Riboflavin metabolism': 3578,
'Drug metabolism - cytochrome P450': 3579,
'Pyruvate metabolism': 3581,
'Drug metabolism - other enzymes': 3582,
'Metabolism of xenobiotics by cytochrome P450': 3428,
'Porphyrin and chlorophyll metabolism': 1170,
'Fc gamma R-mediated phagocytosis': 379,
'Starch and sucrose metabolism': 3429,
'TNF signaling pathway': 1172,
'Phosphatidylinositol signaling system': 2485,
'Sphingolipid signaling pathway': 2487,
'Phospholipase D signaling pathway': 3431,
'Cysteine and methionine metabolism': 3432,
'Inflammatory mediator regulation of TRP channels': 3433,
'JAK-STAT signaling pathway': 3439,
'Focal adhesion': 3440,
'Pentose phosphate pathway': 3441,
'ECM-receptor interaction': 378,
'Retinol metabolism': 2224,
'Cell adhesion molecules (CAMs)': 3442,
'Neuroactive ligand-receptor interaction': 2419,
'Pentose and glucuronate interconversions': 2420,
'Adherens junction': 1746,
'Valine, leucine and isoleucine degradation': 4156,
'Glycosphingolipid biosynthesis - lacto and neolacto series': 2682,
'Sphingolipid metabolism': 2977,
'Glycosphingolipid biosynthesis - globo and isoglobo series': 3469,
'Glycosphingolipid biosynthesis - ganglio series': 1979,
'Salivary secretion': 3471,
'Gastric acid secretion': 1999,
'Long-term depression': 3624,
'Pancreatic secretion': 3474,
'Glycolysis / Gluconeogenesis': 4218,
'Metabolic pathways': 3476,
'Alanine, aspartate and glutamate metabolism': 3911,
'Ubiquinone and other terpenoid-quinone biosynthesis': 3912,
'Renin-angiotensin system': 3915,
'Vitamin digestion and absorption': 441,
'Mineral absorption': 513,
'Cholesterol metabolism': 4135,
'Complement and coagulation cascades': 4136,
'Carbohydrate digestion and absorption': 4137,
'Platelet activation': 4323,
'Protein digestion and absorption': 4301,
'Antigen processing and presentation': 3584,
'Fat digestion and absorption': 4056,
'Bile secretion': 3585,
'Cytokine-cytokine receptor interaction': 4059,
'Viral protein interaction with cytokine and cytokine receptor': 4060,
'Chemokine signaling pathway': 4061,
'Tryptophan metabolism': 3593,
'Glycine, serine and threonine metabolism': 3594,
'FoxO signaling pathway': 1296,
'Olfactory transduction': 1297,
'Toll-like receptor signaling pathway': 1268,
'NF-kappa B signaling pathway': 3834,
'Steroid hormone biosynthesis': 4556,
'Citrate cycle (TCA cycle)': 4561,
'Biosynthesis of amino acids': 4562,
'HIF-1 signaling pathway': 2201,
'C-type lectin receptor signaling pathway': 4564,
'NOD-like receptor signaling pathway': 3914,
'Taste transduction': 3916,
'RIG-I-like receptor signaling pathway': 3904,
'Cytosolic DNA-sensing pathway': 3905,
'Phototransduction': 4228,
'Hippo signaling pathway': 618,
'Vascular smooth muscle contraction': 619,
'mTOR signaling pathway': 4578,
'Hippo signaling pathway - multiple species': 4580,
'Arachidonic acid metabolism': 4582,
'Purine metabolism': 530,
'D-Arginine and D-ornithine metabolism': 531,
'PI3K-Akt signaling pathway': 3607,
'AMPK signaling pathway': 4149,
'Linoleic acid metabolism': 4150,
'Tyrosine metabolism': 4151,
'D-Glutamine and D-glutamate metabolism': 4152,
'alpha-Linolenic acid metabolism': 4153,
'Circadian entrainment': 637,
'Thermogenesis': 638,
'Caffeine metabolism': 4588,
'Carbon metabolism': 1713,
'Nitrogen metabolism': 1714,
'Circadian rhythm': 1715,
'Glutathione metabolism': 4680,
'Aldosterone-regulated sodium reabsorption': 2749,
'Endocrine and other factor-regulated calcium reabsorption': 515,
'Primary bile acid biosynthesis': 4681,
'2-Oxocarboxylic acid metabolism': 886,
'Phenylalanine metabolism': 355,
'Pyrimidine metabolism': 350,
'Glutamatergic synapse': 351,
'Cholinergic synapse': 353,
'Serotonergic synapse': 920,
'Fatty acid metabolism': 2063,
'GABAergic synapse': 4996,
'Sulfur metabolism': 937,
'Long-term potentiation': 939,
'Vasopressin-regulated water reabsorption': 2082,
'Synaptic vesicle cycle': 4998,
'Neurotrophin signaling pathway': 960,
'Proximal tubule bicarbonate reclamation': 4705,
'Retrograde endocannabinoid signaling': 271,
'Dopaminergic synapse': 84,
'VEGF signaling pathway': 964,
'ErbB signaling pathway': 1882,
'Ras signaling pathway': 4476,
'Rap1 signaling pathway': 2047,
'Autophagy - other': 1048,
'Selenocompound metabolism': 1071,
'Apelin signaling pathway': 1072,
'Arginine and proline metabolism': 820,
'SNARE interactions in vesicular transport': 4719,
'MAPK signaling pathway': 4720,
'Growth hormone synthesis, secretion and action': 512,
'Mitophagy - animal': 1097,
'Regulation of actin cytoskeleton': 1098,
'Osteoclast differentiation': 1099,
'Cardiac muscle contraction': 1100,
'Endocytosis': 1264,
'cAMP signaling pathway': 1301,
'Phagosome': 1308,
'Histidine metabolism': 1660,
'Autophagy - animal': 4444,
'Adrenergic signaling in cardiomyocytes': 4808,
'Arginine biosynthesis': 5019,
'Calcium signaling pathway': 4460,
'Protein processing in endoplasmic reticulum': 1681,
'cGMP-PKG signaling pathway': 4818,
'Steroid biosynthesis': 4819,
'Terpenoid backbone biosynthesis': 4821,
'Oocyte meiosis': 4822,
'One carbon pool by folate': 5144,
'TGF-beta signaling pathway': 4823,
'Folate biosynthesis': 1753,
'Cell cycle': 591,
'Insulin secretion': 502,
'GnRH signaling pathway': 4829,
'Taurine and hypotaurine metabolism': 79,
'Ovarian steroidogenesis': 4991,
'Lysine degradation': 533,
'Progesterone-mediated oocyte maturation': 534,
'p53 signaling pathway': 535,
'Insulin signaling pathway': 3501,
'Thyroid hormone signaling pathway': 537,
'Estrogen signaling pathway': 538,
'Melanogenesis': 539,
'Prolactin signaling pathway': 542,
'Thyroid hormone synthesis': 543,
'Sulfur relay system': 2611,
'Axon guidance': 2612,
'Phosphonate and phosphinate metabolism': 2613,
'Glycerolipid metabolism': 1726,
'Glycerophospholipid metabolism': 1727,
'Glucagon signaling pathway': 1728,
'Ether lipid metabolism': 1730,
'Regulation of lipolysis in adipocytes': 3516,
'Inositol phosphate metabolism': 3518,
'Renin secretion': 3520,
'Glycosylphosphatidylinositol (GPI)-anchor biosynthesis': 3595,
'Aldosterone synthesis and secretion': 3530,
'Adipocytokine signaling pathway': 3531,
'Oxytocin signaling pathway': 3502,
'Relaxin signaling pathway': 3503,
'Cortisol synthesis and secretion': 3504,
'Parathyroid hormone synthesis, secretion and action': 3505,
'Apoptosis': 3506,
'Longevity regulating pathway': 3507,
'Longevity regulating pathway - multiple species': 3511,
'Pantothenate and CoA biosynthesis': 3512,
'Notch signaling pathway': 1927,
'beta-Alanine metabolism': 1933,
'Glycosaminoglycan degradation': 1934,
'Cellular senescence': 3513,
'Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate': 1935,
'Butanoate metabolism': 1936,
'Apoptosis - multiple species': 3521,
'Ferroptosis': 1939,
'Glycosaminoglycan biosynthesis - heparan sulfate / heparin': 3522,
'Ribosome biogenesis in eukaryotes': 3524,
'Necroptosis': 3525,
'Biotin metabolism': 612,
'RNA transport': 4403,
'Hedgehog signaling pathway': 1974,
'RNA degradation': 1981,
'Lipoic acid metabolism': 1983,
'mRNA surveillance pathway': 1984}
G_base = nx.Graph()
G_base.add_nodes_from(pathways_names)
G_base.nodes
NodeView(('Oxidative phosphorylation', 'Synthesis and degradation of ketone bodies', 'Biosynthesis of unsaturated fatty acids', 'Intestinal immune network for IgA production', 'Fanconi anemia pathway', 'Wnt signaling pathway', 'Fatty acid degradation', 'Leukocyte transendothelial migration', 'Signaling pathways regulating pluripotency of stem cells', 'Glyoxylate and dicarboxylate metabolism', 'N-Glycan biosynthesis', 'Vitamin B6 metabolism', 'Various types of N-glycan biosynthesis', 'Mucin type O-glycan biosynthesis', 'Mannose type O-glycan biosynthesis', 'Amino sugar and nucleotide sugar metabolism', 'Phenylalanine, tyrosine and tryptophan biosynthesis', 'Nicotinate and nicotinamide metabolism', 'Propanoate metabolism', 'Neomycin, kanamycin and gentamicin biosynthesis', 'Natural killer cell mediated cytotoxicity', 'Fructose and mannose metabolism', 'Tight junction', 'Valine, leucine and isoleucine biosynthesis', 'Galactose metabolism', 'PPAR signaling pathway', 'Ascorbate and aldarate metabolism', 'Homologous recombination', 'Th1 and Th2 cell differentiation', 'Thiamine metabolism', 'Th17 cell differentiation', 'Aminoacyl-tRNA biosynthesis', 'IL-17 signaling pathway', 'Fatty acid biosynthesis', 'Gap junction', 'Fatty acid elongation', 'B cell receptor signaling pathway', 'Fc epsilon RI signaling pathway', 'T cell receptor signaling pathway', 'Riboflavin metabolism', 'Drug metabolism - cytochrome P450', 'Pyruvate metabolism', 'Drug metabolism - other enzymes', 'Metabolism of xenobiotics by cytochrome P450', 'Porphyrin and chlorophyll metabolism', 'Fc gamma R-mediated phagocytosis', 'Starch and sucrose metabolism', 'TNF signaling pathway', 'Phosphatidylinositol signaling system', 'Sphingolipid signaling pathway', 'Phospholipase D signaling pathway', 'Cysteine and methionine metabolism', 'Inflammatory mediator regulation of TRP channels', 'JAK-STAT signaling pathway', 'Focal adhesion', 'Pentose phosphate pathway', 'ECM-receptor interaction', 'Retinol metabolism', 'Cell adhesion molecules (CAMs)', 'Neuroactive ligand-receptor interaction', 'Pentose and glucuronate interconversions', 'Adherens junction', 'Valine, leucine and isoleucine degradation', 'Glycosphingolipid biosynthesis - lacto and neolacto series', 'Sphingolipid metabolism', 'Glycosphingolipid biosynthesis - globo and isoglobo series', 'Glycosphingolipid biosynthesis - ganglio series', 'Salivary secretion', 'Gastric acid secretion', 'Long-term depression', 'Pancreatic secretion', 'Glycolysis / Gluconeogenesis', 'Metabolic pathways', 'Alanine, aspartate and glutamate metabolism', 'Ubiquinone and other terpenoid-quinone biosynthesis', 'Renin-angiotensin system', 'Vitamin digestion and absorption', 'Mineral absorption', 'Cholesterol metabolism', 'Complement and coagulation cascades', 'Carbohydrate digestion and absorption', 'Platelet activation', 'Protein digestion and absorption', 'Antigen processing and presentation', 'Fat digestion and absorption', 'Bile secretion', 'Cytokine-cytokine receptor interaction', 'Viral protein interaction with cytokine and cytokine receptor', 'Chemokine signaling pathway', 'Tryptophan metabolism', 'Glycine, serine and threonine metabolism', 'FoxO signaling pathway', 'Olfactory transduction', 'Toll-like receptor signaling pathway', 'NF-kappa B signaling pathway', 'Steroid hormone biosynthesis', 'Citrate cycle (TCA cycle)', 'Biosynthesis of amino acids', 'HIF-1 signaling pathway', 'C-type lectin receptor signaling pathway', 'NOD-like receptor signaling pathway', 'Taste transduction', 'RIG-I-like receptor signaling pathway', 'Cytosolic DNA-sensing pathway', 'Phototransduction', 'Hippo signaling pathway', 'Vascular smooth muscle contraction', 'mTOR signaling pathway', 'Hippo signaling pathway - multiple species', 'Arachidonic acid metabolism', 'Purine metabolism', 'D-Arginine and D-ornithine metabolism', 'PI3K-Akt signaling pathway', 'AMPK signaling pathway', 'Linoleic acid metabolism', 'Tyrosine metabolism', 'D-Glutamine and D-glutamate metabolism', 'alpha-Linolenic acid metabolism', 'Circadian entrainment', 'Thermogenesis', 'Caffeine metabolism', 'Carbon metabolism', 'Nitrogen metabolism', 'Circadian rhythm', 'Glutathione metabolism', 'Aldosterone-regulated sodium reabsorption', 'Endocrine and other factor-regulated calcium reabsorption', 'Primary bile acid biosynthesis', '2-Oxocarboxylic acid metabolism', 'Phenylalanine metabolism', 'Pyrimidine metabolism', 'Glutamatergic synapse', 'Cholinergic synapse', 'Serotonergic synapse', 'Fatty acid metabolism', 'GABAergic synapse', 'Sulfur metabolism', 'Long-term potentiation', 'Vasopressin-regulated water reabsorption', 'Synaptic vesicle cycle', 'Neurotrophin signaling pathway', 'Proximal tubule bicarbonate reclamation', 'Retrograde endocannabinoid signaling', 'Dopaminergic synapse', 'VEGF signaling pathway', 'ErbB signaling pathway', 'Ras signaling pathway', 'Rap1 signaling pathway', 'Autophagy - other', 'Selenocompound metabolism', 'Apelin signaling pathway', 'Arginine and proline metabolism', 'SNARE interactions in vesicular transport', 'MAPK signaling pathway', 'Growth hormone synthesis, secretion and action', 'Mitophagy - animal', 'Regulation of actin cytoskeleton', 'Osteoclast differentiation', 'Cardiac muscle contraction', 'Endocytosis', 'cAMP signaling pathway', 'Phagosome', 'Histidine metabolism', 'Autophagy - animal', 'Adrenergic signaling in cardiomyocytes', 'Arginine biosynthesis', 'Calcium signaling pathway', 'Protein processing in endoplasmic reticulum', 'cGMP-PKG signaling pathway', 'Steroid biosynthesis', 'Terpenoid backbone biosynthesis', 'Oocyte meiosis', 'One carbon pool by folate', 'TGF-beta signaling pathway', 'Folate biosynthesis', 'Cell cycle', 'Insulin secretion', 'GnRH signaling pathway', 'Taurine and hypotaurine metabolism', 'Ovarian steroidogenesis', 'Lysine degradation', 'Progesterone-mediated oocyte maturation', 'p53 signaling pathway', 'Insulin signaling pathway', 'Thyroid hormone signaling pathway', 'Estrogen signaling pathway', 'Melanogenesis', 'Prolactin signaling pathway', 'Thyroid hormone synthesis', 'Sulfur relay system', 'Axon guidance', 'Phosphonate and phosphinate metabolism', 'Glycerolipid metabolism', 'Glycerophospholipid metabolism', 'Glucagon signaling pathway', 'Ether lipid metabolism', 'Regulation of lipolysis in adipocytes', 'Inositol phosphate metabolism', 'Renin secretion', 'Glycosylphosphatidylinositol (GPI)-anchor biosynthesis', 'Aldosterone synthesis and secretion', 'Adipocytokine signaling pathway', 'Oxytocin signaling pathway', 'Relaxin signaling pathway', 'Cortisol synthesis and secretion', 'Parathyroid hormone synthesis, secretion and action', 'Apoptosis', 'Longevity regulating pathway', 'Longevity regulating pathway - multiple species', 'Pantothenate and CoA biosynthesis', 'Notch signaling pathway', 'beta-Alanine metabolism', 'Glycosaminoglycan degradation', 'Cellular senescence', 'Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate', 'Butanoate metabolism', 'Apoptosis - multiple species', 'Ferroptosis', 'Glycosaminoglycan biosynthesis - heparan sulfate / heparin', 'Ribosome biogenesis in eukaryotes', 'Necroptosis', 'Biotin metabolism', 'RNA transport', 'Hedgehog signaling pathway', 'RNA degradation', 'Lipoic acid metabolism', 'mRNA surveillance pathway'))
G = G_base.copy()
i = 0
while i < len(pathways_names):
j = i + 1
while j < len(pathways_names):
G.add_edge(pathways_names[i], pathways_names[j], weight=df.iloc[pathway_id_name[pathways_names[i]]][pathway_id_name[pathways_names[j]]])
j += 1
i += 1
figure = plt.gcf()
figure.set_size_inches(45, 45)
pos = nx.spring_layout(G)
nx.draw(G,pos)
labels = nx.get_edge_attributes(G,'weight')
nx.draw_networkx_edge_labels(G, pos, edge_labels=labels)
nx.draw(G, pos, node_size=10, font_size=8, with_labels=True)
plt.savefig("./data/graph.png", format="PNG", dpi=100)
plt.show(block=False)

rank_min = 0.05
for u,v,d in G.edges(data=True):
if d["weight"] >= rank_min:
print(f"({u}, {v}, {d})")
(N-Glycan biosynthesis, Various types of N-glycan biosynthesis, {'weight': 0.0573770992007496})
(N-Glycan biosynthesis, Mucin type O-glycan biosynthesis, {'weight': 0.0707253182615287})
(N-Glycan biosynthesis, Mannose type O-glycan biosynthesis, {'weight': 0.0597212678204189})
(N-Glycan biosynthesis, Glycosphingolipid biosynthesis - lacto and neolacto series, {'weight': 0.0584715541181008})
(N-Glycan biosynthesis, Sphingolipid metabolism, {'weight': 0.0610405193633917})
(N-Glycan biosynthesis, Metabolic pathways, {'weight': 0.0594465682158102})
(N-Glycan biosynthesis, Ubiquinone and other terpenoid-quinone biosynthesis, {'weight': 0.0587975071562316})
(N-Glycan biosynthesis, Sulfur metabolism, {'weight': 0.0580601962157386})
(N-Glycan biosynthesis, Steroid biosynthesis, {'weight': 0.059015309166146})
(N-Glycan biosynthesis, Glycosaminoglycan degradation, {'weight': 0.0642060677724785})
(N-Glycan biosynthesis, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0738099748718314})
(N-Glycan biosynthesis, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0716081118952493})
(Mucin type O-glycan biosynthesis, Mannose type O-glycan biosynthesis, {'weight': 0.0553095266975556})
(Mucin type O-glycan biosynthesis, Glycosphingolipid biosynthesis - lacto and neolacto series, {'weight': 0.0537947588502418})
(Mucin type O-glycan biosynthesis, Sphingolipid metabolism, {'weight': 0.0613281838899973})
(Mucin type O-glycan biosynthesis, Metabolic pathways, {'weight': 0.058869029304094})
(Mucin type O-glycan biosynthesis, Ubiquinone and other terpenoid-quinone biosynthesis, {'weight': 0.0598526640635304})
(Mucin type O-glycan biosynthesis, Sulfur metabolism, {'weight': 0.058322506327268})
(Mucin type O-glycan biosynthesis, Steroid biosynthesis, {'weight': 0.0595853173415068})
(Mucin type O-glycan biosynthesis, Glycosaminoglycan degradation, {'weight': 0.0647173864198808})
(Mucin type O-glycan biosynthesis, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0740770293349654})
(Mucin type O-glycan biosynthesis, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0718674562146856})
(Mannose type O-glycan biosynthesis, Glycosphingolipid biosynthesis - lacto and neolacto series, {'weight': 0.0522564187477199})
(Mannose type O-glycan biosynthesis, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0520828951657819})
(Mannose type O-glycan biosynthesis, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0505227329802217})
(Phosphatidylinositol signaling system, Inositol phosphate metabolism, {'weight': 0.0583005670786039})
(Glycosphingolipid biosynthesis - lacto and neolacto series, Glycosphingolipid biosynthesis - globo and isoglobo series, {'weight': 0.0525293773773694})
(Glycosphingolipid biosynthesis - lacto and neolacto series, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.056171087135711})
(Glycosphingolipid biosynthesis - lacto and neolacto series, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0544321529975098})
(Sphingolipid metabolism, Metabolic pathways, {'weight': 0.05186131750713})
(Sphingolipid metabolism, Ubiquinone and other terpenoid-quinone biosynthesis, {'weight': 0.0503981067250449})
(Sphingolipid metabolism, Sulfur metabolism, {'weight': 0.0507302823185234})
(Sphingolipid metabolism, Steroid biosynthesis, {'weight': 0.0509629468624099})
(Sphingolipid metabolism, Glycosaminoglycan degradation, {'weight': 0.0586037932937374})
(Sphingolipid metabolism, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0645843700298778})
(Sphingolipid metabolism, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0626596571229437})
(Metabolic pathways, Glycosaminoglycan degradation, {'weight': 0.0534676137610891})
(Metabolic pathways, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.060829284707146})
(Metabolic pathways, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0586742386139755})
(Ubiquinone and other terpenoid-quinone biosynthesis, Steroid biosynthesis, {'weight': 0.0508570242653279})
(Ubiquinone and other terpenoid-quinone biosynthesis, Glycosaminoglycan degradation, {'weight': 0.0529249804776975})
(Ubiquinone and other terpenoid-quinone biosynthesis, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0608629385816008})
(Ubiquinone and other terpenoid-quinone biosynthesis, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0590564094171132})
(D-Glutamine and D-glutamate metabolism, Proximal tubule bicarbonate reclamation, {'weight': 0.0665720786875216})
(Sulfur metabolism, Glycosaminoglycan degradation, {'weight': 0.0533727361913664})
(Sulfur metabolism, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0613478179242824})
(Sulfur metabolism, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0595367979670519})
(Synaptic vesicle cycle, Endocytosis, {'weight': 0.0544521464900184})
(Steroid biosynthesis, Glycosaminoglycan degradation, {'weight': 0.0534768227609683})
(Steroid biosynthesis, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.061484261468451})
(Steroid biosynthesis, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0596651102801799})
(Lysine degradation, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0510869874607356})
(Pantothenate and CoA biosynthesis, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0501662935779906})
(Pantothenate and CoA biosynthesis, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0525443320102646})
(Glycosaminoglycan degradation, Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, {'weight': 0.0731609591897241})
(Glycosaminoglycan degradation, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0722583446694861})
(Glycosaminoglycan biosynthesis - chondroitin sulfate / dermatan sulfate, Glycosaminoglycan biosynthesis - heparan sulfate / heparin, {'weight': 0.0853757701406303})
(RNA transport, mRNA surveillance pathway, {'weight': 0.0567603578699123})